Middle School Math Quiz: Interpret Inequalities On Number Lines
20 questions · exam conditions
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Interpret Inequalities On Number LinesQuestion 1 of 20

A number line shows points labeled −7-7, −3-3, 00, 22, and 55. Which list shows these numbers in order from least to greatest (left to right on the number line)?

−7, 0, −3, 2, 5-7,\,0,\,-3,\,2,\,5
−3, −7, 0, 2, 5-3,\,-7,\,0,\,2,\,5
5, 2, 0, −3, −75,\,2,\,0,\,-3,\,-7
−7, −3, 0, 2, 5-7,\,-3,\,0,\,2,\,5
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Middle School Math Quiz

Middle School Math Quiz: Interpret Inequalities On Number Lines

Practice Interpret Inequalities On Number Lines in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Interpret Inequalities On Number Lines, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

A number line shows points labeled −7-7, −3-3, 00, 22, and 55. Which list shows these numbers in order from least to greatest (left to right on the number line)?

  1. −7, 0, −3, 2, 5-7,\,0,\,-3,\,2,\,5
  2. −3, −7, 0, 2, 5-3,\,-7,\,0,\,2,\,5
  3. 5, 2, 0, −3, −75,\,2,\,0,\,-3,\,-7
  4. −7, −3, 0, 2, 5-7,\,-3,\,0,\,2,\,5 (correct answer)
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is left of b (a smaller, b larger), understanding left-to-right increases, comparing signed numbers. Number line interpretation: a < b means a positioned left of b on number line (a is smaller value, b is larger, left < right); examples: 5 > 3 (5 right of 3, farther from zero for positives means greater), -2 > -5 (-2 right of -5, closer to zero for negatives means less negative thus greater: -2 is warmer than -5°C, higher than -5 m below sea level), 2 > -3 (positive 2 right of negative -3, any positive > any negative); order: increasing from left to right (-7 < -3 < 0 < 2 < 5 arranged left to right on line shows least to greatest). For example, inequality -3 > -7 on number line: -7 is farther left (more negative, smaller), -3 is closer to zero (less negative, greater), so -3 positioned right of -7, inequality -3 > -7 means -3 is right of -7; or 5 > 3 shows 5 right of 3 (both positive, 5 farther from zero is larger); or order -5, -2, 0, 3 from least to greatest: positions left-to-right: -5 leftmost (smallest), then -2, then 0, then 3 rightmost (largest). The correct order from least to greatest is -7, -3, 0, 2, 5, matching choice C. A common error is wrong ordering like starting with -3 before -7 (choice A), descending order (choice B), or misplaced zero and -3 (choice D), not arranging left-to-right properly. Interpreting: inequality symbol shows position (< means left of, > means right of), greater value is farther right (for positives: larger number farther from zero; for negatives: less negative is greater, closer to zero is right). Comparing signed: same sign (magnitudes for positives: 5 > 3, |-7| > |-3| but -7 < -3 because farther left), different signs (positive always > negative: 1 > -100); ordering: arrange left-to-right for least-to-greatest (start with most negative, end with most positive); number line as tool: visual shows order (left < right), helps compare signed numbers (plot both, see which is right); mistakes: reversing greater/less with position, magnitude error for negatives, zero position wrong, direction confused.

Question 2

A student writes the inequality 5>35>3 to compare two scores. What does 5>35>3 mean on a number line?

  1. 5 is to the left of 3 on the number line, so 5 is less than 3.
  2. 5 is to the right of 3 on the number line, so 5 is greater than 3. (correct answer)
  3. 5 and 3 are the same point on the number line because they are both positive.
  4. 3 is to the right of 5 on the number line, so 5 is less than 3.
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. In number line interpretation, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left being less than right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater, like -2°C being warmer than -5°C), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For the inequality 5 > 3 on a number line, 3 is farther left (smaller positive, closer to zero), 5 is to the right (larger positive, farther from zero), so 5 is positioned to the right of 3, meaning 5 > 3 indicates 5 is greater than 3. The correct interpretation is that 5 is to the right of 3 on the number line, so 5 is greater than 3, which matches choice B. A common error is reversing positions, like claiming 5 is to the left of 3 so 5 is less (as in choice A or D), or thinking they are the same because both positive (choice C), ignoring that left-to-right order properly shows increasing values. When interpreting, the inequality symbol shows position (> means right of, < means left of), with greater values farther right (for positives, larger numbers are farther from zero); comparing signed numbers involves magnitudes for positives like 5 > 3, but for negatives, being closer to zero means greater, and positives are always greater than negatives. Ordering uses left-to-right for least-to-greatest, starting with smaller numbers; the number line visually shows this order (left < right), helping compare values by seeing which is to the right, with mistakes like confusing direction or zero's position.

Question 3

A scuba diver is at an elevation of −3-3 meters (below sea level), and a buoy is at 22 meters (above sea level). Which inequality correctly matches their positions on a number line?

  1. 2>−32>-3 because 2 is to the right of −3-3 on the number line. (correct answer)
  2. −3>2-3>2 because 3 is greater than 2.
  3. 2<−32<-3 because negative numbers are always greater than positive numbers.
  4. −3=2-3=2 because they are the same distance from 0.
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. On a number line, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left < right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater, like -2°C is warmer than -5°C), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For comparing -3 and 2 on the number line, -3 is to the left (negative, smaller), 2 is to the right (positive, larger), so 2 is positioned to the right of -3, meaning 2 > -3; this fits the elevations where 2 m above is higher than -3 m below sea level. The correct inequality is 2 > -3 because 2 is to the right of -3 on the number line, which is choice B. A common error is magnitude comparison ignoring signs, like -3 > 2 because 3 > 2 (but negative is smaller), or claiming negatives are always greater than positives (reversing order), or thinking same distance means equal (but directions differ). When interpreting, the inequality symbol indicates position (< means left of, > means right of), and for different signs, positives are always greater than negatives like 2 > -3 since positives are to the right; ordering starts with most negative leftmost to most positive rightmost. The number line is a tool to show this visually (left < right), helping compare signed numbers by plotting and seeing which is to the right, avoiding mistakes like direction confusion or zero position errors.

Question 4

A student says, "−7>−3-7>-3 because 7>37>3." Which statement correctly fixes the student's reasoning using the number line?

  1. The student is correct because numbers farther from 00 are always greater.
  2. The student is incorrect because on a number line −7-7 is left of −3-3, so −7<−3-7<-3. (correct answer)
  3. The student is incorrect because all negative numbers are equal.
  4. The student is correct because the number with the bigger absolute value is always greater.
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is left of b (a smaller, b larger), understanding left-to-right increases, comparing signed numbers. Number line interpretation: a < b means a positioned left of b on number line (a is smaller value, b is larger, left < right); examples: 5 > 3 (5 right of 3, farther from zero for positives means greater), -2 > -5 (−2 right of -5, closer to zero for negatives means less negative thus greater: -2 is warmer than -5°C, higher than -5 m below sea level), 2 > -3 (positive 2 right of negative -3, any positive > any negative); order: increasing from left to right (-7 < -3 < 0 < 2 < 5 arranged left to right on line shows least to greatest). For example, inequality -3 > -7 on number line: -7 is farther left (more negative, smaller), -3 is closer to zero (less negative, greater), so -3 positioned right of -7, inequality -3 > -7 means -3 is right of -7; or 5 > 3 shows 5 right of 3 (both positive, 5 farther from zero is larger); or order -5, -2, 0, 3 from least to greatest: positions left-to-right: -5 leftmost (smallest), then -2, then 0, then 3 rightmost (largest). The correct fix is that the student is incorrect because on a number line -7 is left of -3, so -7 < -3, matching choice B. A common error is magnitude comparison for negatives like -7 > -3 because | -7 | > | -3 | or farther from 0 is greater (choices A and D), or thinking all negatives are equal (choice C). Interpreting: inequality symbol shows position (< means left of, > means right of), greater value is farther right (for positives: larger number farther from zero; for negatives: less negative is greater, closer to zero is right). Comparing signed: same sign (magnitudes for positives: 5 > 3, |-7| > |-3| but -7 < -3 because farther left), different signs (positive always > negative: 1 > -100); ordering: arrange left-to-right for least-to-greatest (start with most negative, end with most positive); number line as tool: visual shows order (left < right), helps compare signed numbers (plot both, see which is right); mistakes: reversing greater/less with position, magnitude error for negatives, zero position wrong, direction confused.

Question 5

A coach records two times (in seconds) relative to a target time: −2-2 (2 seconds faster than the target) and −2-2 (also 2 seconds faster). Which statement is true and correctly uses number-line position language?

  1. −2<−2-2<-2 because negative numbers are always less than themselves.
  2. −2>−2-2>-2 because the first −2-2 is to the right of the second −2-2.
  3. −2≤−2-2\le -2 is false because ≤\le only works for different numbers.
  4. −2≥−2-2\ge -2 because both values are at the same point on the number line. (correct answer)
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is left of b (a smaller, b larger), understanding left-to-right increases, comparing signed numbers. Number line interpretation: a < b means a positioned left of b on number line (a is smaller value, b is larger, left < right); examples: 5 > 3 (5 right of 3, farther from zero for positives means greater), -2 > -5 (−2 right of -5, closer to zero for negatives means less negative thus greater: -2 is warmer than -5°C, higher than -5 m below sea level), 2 > -3 (positive 2 right of negative -3, any positive > any negative); order: increasing from left to right (-7 < -3 < 0 < 2 < 5 arranged left to right on line shows least to greatest). For example, inequality -3 > -7 on number line: -7 is farther left (more negative, smaller), -3 is closer to zero (less negative, greater), so -3 positioned right of -7, inequality -3 > -7 means -3 is right of -7; or 5 > 3 shows 5 right of 3 (both positive, 5 farther from zero is larger); or order -5, -2, 0, 3 from least to greatest: positions left-to-right: -5 leftmost (smallest), then -2, then 0, then 3 rightmost (largest). The correct statement is -2 ≥ -2 because both values are at the same point on the number line, matching choice A. A common error is claiming strict inequality like > or < for equals (choices B and C), or thinking ≤ is false for same numbers (choice D). Interpreting: inequality symbol shows position (< means left of, > means right of), greater value is farther right (for positives: larger number farther from zero; for negatives: less negative is greater, closer to zero is right). Comparing signed: same sign (magnitudes for positives: 5 > 3, |-7| > |-3| but -7 < -3 because farther left), different signs (positive always > negative: 1 > -100); ordering: arrange left-to-right for least-to-greatest (start with most negative, end with most positive); number line as tool: visual shows order (left < right), helps compare signed numbers (plot both, see which is right); mistakes: reversing greater/less with position, magnitude error for negatives, zero position wrong, direction confused.

Question 6

Two inequalities are graphed on the same number line: m≥−1m ≥ -1 and n\<3n \< 3. If point PP represents a value that satisfies both inequalities simultaneously, which description is most accurate?

  1. Point PP can be located anywhere from −1-1 to 33, including both endpoint values on the number line
  2. Point PP can be located anywhere from −1-1 to 33, including −1-1 but not including 33 on the number line (correct answer)
  3. Point PP must be located exactly at 11 since that's the middle value between −1-1 and 33
  4. Point PP can be any value less than −1-1 or any value greater than 33 on the number line
Explanation: The correct answer is B. To satisfy both inequalities simultaneously, we need the intersection: m≥−1m ≥ -1 AND n\<3n \< 3. This means −1≤P\<3-1 ≤ P \< 3, which includes −1-1 (due to the ≥ symbol) but excludes 33 (due to the < symbol). Choice A incorrectly includes 33. Choice C incorrectly assumes only one value works. Choice D describes values that satisfy neither inequality or only one of them.

Question 7

Marcus writes the inequality −2.5>y-2.5 > y to represent the temperature in his freezer. Based on the number line shown, which statement correctly interprets this inequality?

  1. The temperature yy is warmer than −2.5-2.5 degrees, so it includes values like −2-2, −1-1, and 00
  2. The temperature yy is colder than −2.5-2.5 degrees, so it includes values like −3-3, −4-4, and −5-5 (correct answer)
  3. The temperature yy is exactly −2.5-2.5 degrees since that's what the inequality symbol points to
  4. The temperature yy is between −3-3 and −2-2 degrees since −2.5-2.5 is in that range
Explanation: The correct answer is B. The inequality −2.5>y-2.5 > y means y<−2.5y < -2.5, so the temperature is less than (colder than) −2.5-2.5 degrees. On a number line, this includes all values to the left of −2.5-2.5, such as −3-3, −4-4, −5-5, etc. Choice A incorrectly reverses the inequality direction. Choice C misunderstands that inequalities represent ranges, not single values. Choice D incorrectly limits the solution to a specific interval.

Question 8

Look at the number line diagram. Point RR is marked, and the shaded region represents all values of xx where x≤Rx ≤ R. If R=1.5R = 1.5, which number would NOT be included in the shaded region?

  1. The value 1.51.5 because the inequality uses ≤ which excludes the boundary point
  2. The value 2.02.0 because it is greater than 1.51.5 and falls outside the inequality (correct answer)
  3. The value 0.50.5 because it is less than 1.51.5 and falls outside the inequality
  4. The value −1.0-1.0 because negative numbers cannot satisfy inequalities with positive boundaries
Explanation: The correct answer is B. The inequality x≤1.5x ≤ 1.5 includes all values less than or equal to 1.51.5. The value 2.02.0 is greater than 1.51.5, so it does not satisfy x≤1.5x ≤ 1.5 and would not be in the shaded region. Choice A incorrectly states that ≤ excludes the boundary (it includes it). Choice C incorrectly excludes 0.50.5 when 0.5≤1.50.5 ≤ 1.5 is true. Choice D incorrectly suggests negative numbers can't satisfy the inequality when −1.0≤1.5-1.0 ≤ 1.5 is true.

Question 9

Consider the number line shown with points marked at specific locations. If point MM represents −32-\frac{3}{2} and point NN represents 52\frac{5}{2}, which inequality correctly describes the relationship between these points?

  1. M>NM > N because −32-\frac{3}{2} appears to the left of 52\frac{5}{2} on the number line diagram
  2. M<NM < N because −32-\frac{3}{2} is positioned to the left of 52\frac{5}{2} on the number line diagram (correct answer)
  3. M=NM = N because both points are the same distance from zero on the number line diagram
  4. M≥NM ≥ N because negative fractions are always greater than or equal to positive fractions in inequalities
Explanation: The correct answer is B. On a number line, values increase from left to right. Since MM at −32=−1.5-\frac{3}{2} = -1.5 is positioned to the left of NN at 52=2.5\frac{5}{2} = 2.5, we have M<NM < N, or −32<52-\frac{3}{2} < \frac{5}{2}. Choice A incorrectly reverses the inequality direction. Choice C confuses distance from zero with equality (∣−1.5∣≠∣2.5∣|-1.5| ≠ |2.5| anyway). Choice D makes a false general statement about negative and positive numbers.

Question 10

A weather station records temperatures where t≥−5t ≥ -5 represents safe operating conditions. On the same day, equipment malfunction occurs when t>8t > 8. For what range of temperatures tt does the station operate safely without equipment malfunction?

  1. All temperatures where t<−5t < -5 or t≤8t ≤ 8, representing the combination of both conditions
  2. All temperatures where −5≤t≤8-5 ≤ t ≤ 8, representing the overlap of safe operation and no malfunction (correct answer)
  3. All temperatures where −5<t<8-5 < t < 8, representing the strict boundaries of both operating conditions
  4. All temperatures where t≥8t ≥ 8 or t≤−5t ≤ -5, representing either condition being satisfied independently
Explanation: The correct answer is B. Safe operation requires t≥−5t ≥ -5 AND no malfunction requires t≤8t ≤ 8 (the opposite of t>8t > 8). Both conditions must be satisfied simultaneously, giving us −5≤t≤8-5 ≤ t ≤ 8. Choice A incorrectly uses OR instead of AND and wrong inequality directions. Choice C incorrectly excludes the boundary values −5-5 and 88. Choice D describes conditions where at least one problem occurs (either too cold or malfunction), not safe operation.

Question 11

Study the number line diagram where two different inequalities are represented by different line styles. If the solid line represents x≥0x ≥ 0 and the dashed line represents x<4x < 4, what does the overlapping region represent?

  1. The solution x≥4x ≥ 4 because that's where both line styles meet at their boundary
  2. The solution 0≤x<40 ≤ x < 4 because that's where both inequality conditions are satisfied together (correct answer)
  3. The solution x<0x < 0 or x≥4x ≥ 4 because those are the non-overlapping regions on the diagram
  4. The solution 0<x≤40 < x ≤ 4 because the overlapping excludes both boundary points from the inequalities
Explanation: The correct answer is B. The overlapping region represents where both inequalities are true simultaneously: x≥0x ≥ 0 AND x<4x < 4, which gives us 0≤x<40 ≤ x < 4. This includes 00 (from ≥) but excludes 44 (from <). Choice A only describes the boundary point. Choice C describes the union of non-overlapping regions, not the intersection. Choice D incorrectly excludes 00 and incorrectly includes 44.

Question 12

A student says: "Since −6-6 is farther from 0 than −1-1, −6-6 must be greater." Which inequality correctly compares the numbers on a number line?

  1. −6>−1-6>-1 because farther from 0 means greater for negative numbers.
  2. −6=−1-6=-1 because both are negative.
  3. −6<−1-6<-1 because −6-6 is to the left of −1-1 on the number line. (correct answer)
  4. −6>−1-6>-1 because left is greater on a number line.
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. In number line interpretation, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left being less than right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For -6 and -1 on a number line, -6 is farther left (more negative, smaller), -1 is closer to zero (less negative, greater), so -1 is to the right of -6, meaning -6 < -1 corrects the student's magnitude error. The correct inequality is -6 < -1 because -6 is to the left of -1 on the number line, which matches choice B. A common error is claiming farther from 0 means greater for negatives (choice A), or equal because negative (choice C), or left greater (choice D), like magnitude comparison where |-6| > |-1| but actually -6 < -1. Interpreting uses > for right of, with greater farther right (for negatives, closer to zero); comparing same sign: farther left is smaller. Mistakes include magnitude error for negatives or reversing position.

Question 13

Examine the number line representation shown. The inequality k>−2k > -2 is graphed with appropriate markings. Which value of kk would be closest to the boundary but still satisfy the inequality?

  1. The value k=−2k = -2 because it is exactly at the boundary point marked on the number line
  2. The value k=−1.9k = -1.9 because it is slightly greater than −2-2 and very close to the boundary (correct answer)
  3. The value k=−2.1k = -2.1 because it is very close to −2-2 and satisfies the inequality condition
  4. The value k=0k = 0 because it is the first positive integer greater than the boundary point
Explanation: The correct answer is B. The inequality k>−2k > -2 requires kk to be strictly greater than −2-2, which excludes −2-2 itself. Among the values that satisfy this inequality, k=−1.9k = -1.9 is the closest to the boundary at −2-2. Choice A incorrectly includes −2-2, which doesn't satisfy k>−2k > -2. Choice C gives −2.1-2.1, which is less than −2-2 and doesn't satisfy the inequality. Choice D gives a value that satisfies the inequality but is not closest to the boundary.

Question 14

The inequality y≤3.5y ≤ 3.5 is graphed on a number line. Jamie claims that 3143\frac{1}{4} is a solution, while Alex claims that 3.63.6 is a solution. Who is correct and why?

  1. Jamie is correct because 314=3.25<3.53\frac{1}{4} = 3.25 < 3.5, but Alex is wrong because 3.6>3.53.6 > 3.5 (correct answer)
  2. Alex is correct because 3.63.6 rounds to 44 which satisfies the inequality, but Jamie is wrong about fractions
  3. Both are correct because the inequality y≤3.5y ≤ 3.5 includes all values close to 3.53.5 on the number line
  4. Neither is correct because only integer values can satisfy inequalities written in decimal form like y≤3.5y ≤ 3.5
Explanation: The correct answer is A. The inequality y≤3.5y ≤ 3.5 means yy can be any value less than or equal to 3.53.5. Jamie's value 314=3.253\frac{1}{4} = 3.25 satisfies this since 3.25≤3.53.25 ≤ 3.5. Alex's value 3.63.6 does not satisfy this since 3.6>3.53.6 > 3.5. Choice B incorrectly suggests rounding changes inequality relationships. Choice C incorrectly suggests 'closeness' rather than the actual inequality relationship. Choice D incorrectly restricts solutions to integers only.

Question 15

A number line is drawn. Point xx is at −8-8 and point yy is at −8-8. Which statement is true?

  1. x<yx<y because the left side of the number line is greater.
  2. x≥yx\ge y is false because negative numbers cannot be equal.
  3. x≤yx\le y because both points are at the same position on the number line. (correct answer)
  4. x>yx>y because −8-8 is to the right of −8-8.
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. In number line interpretation, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left being less than right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For points x and y both at -8 on a number line, they are at the same position, so x = y, meaning inequalities like x <= y or x >= y are true since they include equality. The correct statement is x <= y because both points are at the same position on the number line, which matches choice B. A common error is claiming x > y despite same (choice A), or x < y with left greater (choice C), or x >= y false because negative (choice D), ignoring equality for negatives. When interpreting equals, <= or >= apply; comparing same negatives shows equality like positives. The number line helps by showing identical spots, with mistakes like assuming negatives can't equal or direction issues.

Question 16

In a science lab, one thermometer reads 2∘C2^\circ\text{C} and another reads −3∘C-3^\circ\text{C}. Which inequality correctly compares the temperatures, and what does it mean on a number line?

  1. −3>2-3>2 because negative numbers are always greater than positive numbers.
  2. 2>−32>-3 because 22 is to the right of −3-3 on the number line. (correct answer)
  3. 2<−32<-3 because −3-3 is farther from 00.
  4. 2=−32=-3 because they are on opposite sides of 00.
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is left of b (a smaller, b larger), understanding left-to-right increases, comparing signed numbers. Number line interpretation: a < b means a positioned left of b on number line (a is smaller value, b is larger, left < right); examples: 5 > 3 (5 right of 3, farther from zero for positives means greater), -2 > -5 (−2 right of -5, closer to zero for negatives means less negative thus greater: -2 is warmer than -5°C, higher than -5 m below sea level), 2 > -3 (positive 2 right of negative -3, any positive > any negative); order: increasing from left to right (-7 < -3 < 0 < 2 < 5 arranged left to right on line shows least to greatest). For example, inequality -3 > -7 on number line: -7 is farther left (more negative, smaller), -3 is closer to zero (less negative, greater), so -3 positioned right of -7, inequality -3 > -7 means -3 is right of -7; or 5 > 3 shows 5 right of 3 (both positive, 5 farther from zero is larger); or order -5, -2, 0, 3 from least to greatest: positions left-to-right: -5 leftmost (smallest), then -2, then 0, then 3 rightmost (largest). The correct interpretation is 2 > -3 because 2 is to the right of -3 on the number line, matching choice B. A common error is claiming negatives are always greater than positives (choice A or D), or that being farther from 0 makes -3 greater (choice C), or they are equal due to opposite sides (choice D). Interpreting: inequality symbol shows position (< means left of, > means right of), greater value is farther right (for positives: larger number farther from zero; for negatives: less negative is greater, closer to zero is right). Comparing signed: same sign (magnitudes for positives: 5 > 3, |-7| > |-3| but -7 < -3 because farther left), different signs (positive always > negative: 1 > -100); ordering: arrange left-to-right for least-to-greatest (start with most negative, end with most positive); number line as tool: visual shows order (left < right), helps compare signed numbers (plot both, see which is right); mistakes: reversing greater/less with position, magnitude error for negatives, zero position wrong, direction confused.

Question 17

A student's account balance is $0 and another student's balance is $-4 (they owe $4). Which statement is true on a number line?

  1. 0<−40<-4 because 0 is the smallest number.
  2. 0>−40>-4 because 0 is to the right of −4-4 on the number line. (correct answer)
  3. 0=−40=-4 because both are not positive.
  4. −4>0-4>0 because 4 is greater than 0.
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. On a number line, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left < right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater, like -2 is higher than -5 m below sea level), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For comparing 0 and -4 on the number line, -4 is to the left (negative, smaller), 0 is to the right (greater), so 0 is positioned to the right of -4, meaning 0 > -4; this matches account balances where $0 is better than owing $4. The correct statement is 0 > -4 because 0 is to the right of -4 on the number line, which is choice B. A common error is thinking zero is the smallest (ignoring negatives are smaller), or magnitude like -4 > 0 because 4 > 0 (ignoring sign), or claiming equality because both not positive. When interpreting, the inequality symbol shows position (< means left of, > means right of), and zero is greater than negatives since it's to their right; for different signs, positive (including zero) > negative. The number line visualizes order (left < right), helping compare by plotting points and seeing which is right, avoiding mistakes like zero as smallest or direction confused.

Question 18

A submarine is at −4-4 meters (below sea level) and the surface is at 00 meters. Which statement correctly interprets 0>−40>-4 on a number line?

  1. 0 is to the left of −4-4 on the number line, so 0 is greater.
  2. 0 is to the right of −4-4 on the number line, so 0 is greater. (correct answer)
  3. −4-4 is greater because 4 is larger than 0.
  4. 0 is the smallest number, so it must be less than −4-4.
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. In number line interpretation, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left being less than right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater, like higher than -5 m below sea level), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For the inequality 0 > -4 on a number line, -4 is to the left (negative, below surface), 0 is to the right (at surface, greater), so 0 > -4 means 0 is positioned to the right of -4. The correct interpretation is that 0 is to the right of -4 on the number line, so 0 is greater, which matches choice B. A common error is claiming 0 left of -4 so greater (choice A), or -4 greater because 4 > 0 (choice C), or 0 smallest ignoring negatives (choice D), not arranging left-to-right properly. Interpreting uses inequality symbols for position (> means right of), with greater farther right; comparing different signs shows positive (including 0) > negative. The number line visually shows order, helping plot and see right is greater, with mistakes like direction confusion or zero as smallest.

Question 19

A student says, "Because ∣−8∣>∣−2∣|-8|>|-2|, the inequality −8>−2-8>-2 must be true." Which statement correctly fixes the student's reasoning using the number line?

  1. The student is correct; a larger absolute value always means a larger number.
  2. The student is incorrect; −8-8 is to the left of −2-2 on the number line, so −8<−2-8<-2. (correct answer)
  3. The student is incorrect; −8-8 and −2-2 cannot be compared because they are negative.
  4. The student is correct; numbers increase as you move left, so −8>−2-8>-2.
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. On a number line, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left < right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater, like -2°C is warmer than -5°C), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For the student's claim about -8 and -2, |-8| > |-2| is true, but on the number line, -8 is to the left of -2 (more negative, smaller), -2 is right (less negative, greater), so -8 < -2, not >. The correct fix is that the student is incorrect; -8 is to the left of -2 on the number line, so -8 < -2, which is choice B. A common error is magnitude comparison for negatives, like assuming larger absolute value means larger number (but for negatives, it's smaller, like -8 < -2), or thinking numbers increase leftward, or that negatives can't be compared. When interpreting, the inequality symbol shows position (< means left of, > means right of), and for negatives, larger magnitude means smaller value and farther left, like |-8| > |-2| but -8 < -2; comparing same-sign, magnitudes reverse for negatives. The number line helps visualize (left < right), aiding in seeing the right one is greater, avoiding mistakes like magnitude errors or position reversal.

Question 20

A number line shows point AA at 00 and point BB at 77. Which inequality and interpretation are correct?

  1. 0<70<7 because 0 is to the left of 7 on the number line. (correct answer)
  2. 0=70=7 because both are nonnegative.
  3. 0≥70\ge 7 because 0 is closer to 0 than 7 is.
  4. 0>70>7 because 0 is the starting point of the number line.
Explanation: This question tests interpreting inequalities as position statements on a number line: a < b means a is to the left of b (a is smaller, b is larger), understanding that values increase from left to right, including comparing signed numbers. On a number line, a < b means a is positioned to the left of b (a has a smaller value, b is larger, with left < right); for example, 5 > 3 because 5 is to the right of 3 (farther from zero for positives means greater), -2 > -5 because -2 is to the right of -5 (closer to zero for negatives means less negative and thus greater, like -2°C is warmer than -5°C), and 2 > -3 because positive 2 is to the right of negative -3 (any positive is greater than any negative), with order increasing from left to right such as -7 < -3 < 0 < 2 < 5 arranged left to right showing least to greatest. For points A at 0 and B at 7 on the number line, 0 is to the left (smaller), 7 is to the right (larger, farther from zero), so 0 is left of 7, meaning 0 < 7. The correct inequality is 0 < 7 because 0 is to the left of 7 on the number line, which is choice B. A common error is thinking 0 > 7 as starting point (but 0 is smaller), or equality because nonnegative, or ≥ because closer to zero (but closer means smaller here for positives). When interpreting, the inequality symbol shows position (< means left of, > means right of), and for positives, larger is farther right like 7 > 0; comparing, plot to see right is greater. The number line visualizes order (left < right), helping avoid mistakes like zero position wrong or direction confused.