6th Grade Math Quiz: Write And Represent Simple Inequalities

What this quiz covers

This quiz focuses on Write And Represent Simple Inequalities, giving you a quick way to practice the rules, question types, and explanations that matter most for 6th Grade 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.

Question 1

1. $b>6$
2. $b\ge 6$
3. $b\le 6$ (correct answer)
4. $b<6$

Question 2

1. $w < 350$ because the additional weight must be strictly less than 350 pounds
2. $w \leq 350$ because the total weight cannot exceed the maximum capacity (correct answer)
3. $w > 350$ because more than 350 pounds can safely be added
4. $w \geq 350$ because at least 350 pounds of space remains available

Question 3

1. $x\ge 50$
2. $x>50$
3. $x<50$
4. $x\le 50$ (correct answer)

Question 4

1. $t<9$; open circle at 9 and shading to the left (correct answer)
2. $t\ge 9$; closed circle at 9 and shading to the right
3. $t>9$; open circle at 9 and shading to the right
4. $t\le 9$; closed circle at 9 and shading to the left

Question 5

1. $x>40$; you may spend more than $40 only.
2. $x\ge 40$; you must spend $40 or more.
3. $x\le 40$; any amount up to and including $40 works (infinitely many possible dollar amounts). (correct answer)
4. $x<40$; you may spend any amount under $40 but not $40.

Question 6

1. $x<60$ (correct answer)
2. $x>60$
3. $x\ge 60$
4. $x\le 60$

Question 7

1. Because $x>6$ has no solutions since you cannot buy more than 6 bottles.
2. Because $x>6$ is true for exactly 6 values of $x$.
3. Because $x>6$ is true for $x=7,8,9,10,\dots$, and there is no largest number of bottles you could buy. (correct answer)
4. Because $x>6$ is true only for $x=7$, so there is one solution.

Question 8

1. $w\le 20$; closed circle at 20 and shading left (correct answer)
2. $w\ge 20$; closed circle at 20 and shading right
3. $w>20$; open circle at 20 and shading right
4. $w<20$; open circle at 20 and shading left

Question 9

1. The inequality is $a\ge 13$, and it has infinitely many solutions: any age 13 or older. (correct answer)
2. The inequality is $a\le 13$, and it has infinitely many solutions: any age 13 or younger.
3. The inequality is $a\ge 13$, and it has exactly 13 solutions.
4. The inequality is $a>13$, and it has only one solution: $a=14$.

Question 10

1. $x \leq 4$ because the circle is closed and shading goes left
2. $x \geq 4$ because the circle is closed and shading goes right (correct answer)
3. $x < 4$ because the shading does not include numbers greater than 4
4. $x > 4$ because the circle shows 4 is included in the solution

Question 11

1. $t > 75$ where $t$ is temperature in degrees Fahrenheit (correct answer)
2. $t \geq 75$ where $t$ is temperature in degrees Fahrenheit
3. $t < 75$ where $t$ is temperature in degrees Fahrenheit
4. $t \leq 75$ where $t$ is temperature in degrees Fahrenheit

Question 12

1. All numbers to the left of -2, including -2 itself, are solutions to the inequality
2. All numbers to the left of -2, not including -2, are solutions to the inequality (correct answer)
3. Only negative integers less than -2 are solutions to the inequality
4. All numbers between -2 and positive infinity are solutions to the inequality

Question 13

1. Yes, because the y-coordinate 0 satisfies the inequality $y > -1$ regardless of x-coordinate (correct answer)
2. No, because the point $(-2, 0)$ is not in the shaded region above $y = -1$
3. No, because negative x-coordinates cannot be solutions to inequalities involving y
4. Yes, because both coordinates must be positive for the point to be a solution

Question 14

1. Inequality: $a>13$; Number line: open circle at 13, shaded to the right
2. Inequality: $a<13$; Number line: open circle at 13, shaded to the left
3. Inequality: $a\le 13$; Number line: closed circle at 13, shaded to the left
4. Inequality: $a\ge 13$; Number line: closed circle at 13, shaded to the right (correct answer)

Question 15

1. $x\le 50$; number line: open circle at 50 and shading to the left
2. $x\ge 50$; number line: closed circle at 50 and shading to the left
3. $x\le 50$; number line: closed circle at 50 and shading to the right
4. $x\le 50$; number line: closed circle at 50 and shading to the left (correct answer)

Question 16

1. Open circle at 75, shaded to the right (correct answer)
2. Open circle at 75, shaded to the left
3. Closed circle at 75, shaded to the left
4. Closed circle at 75, shaded to the right

Question 17

1. $0.25q > 0.75$; Sarah needs more than 3 quarters, so at least 4 quarters (correct answer)
2. $0.25q \geq 0.75$; Sarah needs at least 3 quarters to operate the meter
3. $0.25q < 0.75$; Sarah needs fewer than 3 quarters to operate the meter
4. $q > 0.75$; Sarah needs more than 0.75 quarters to operate the meter

Question 18

1. $r + 15 > 40$ because she must exceed the two-day minimum
2. $r + 15 \geq 40$ because she must meet or exceed the minimum (correct answer)
3. $r \geq 20$ because each day has an independent 20-minute requirement
4. $r + 15 \geq 35$ because the total must be at least 40 minutes

Question 19

1. $a>13$
2. $a\ge 13$ (correct answer)
3. $a<13$
4. $a\le 13$

Question 20

1. $s\ge 75$
2. $s<75$
3. $s>75$ (correct answer)
4. $s\le 75$