Inequalities & Absolute Value - ACT Math
Card 1 of 30
What is the solution to $|3x+6|<9$?
What is the solution to $|3x+6|<9$?
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$-5<x<1$. Solve $-9 < 3x+6 < 9$, then divide by $3$.
$-5<x<1$. Solve $-9 < 3x+6 < 9$, then divide by $3$.
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Solve for $x$: $|x + 7| > 4$.
Solve for $x$: $|x + 7| > 4$.
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$x > -3$ or $x < -11$. Distance from -7 exceeds 4 units.
$x > -3$ or $x < -11$. Distance from -7 exceeds 4 units.
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What inequality corresponds to the interval $[-3,7)$?
What inequality corresponds to the interval $[-3,7)$?
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$-3\le x<7$. Bracket includes $-3$, parenthesis excludes $7$.
$-3\le x<7$. Bracket includes $-3$, parenthesis excludes $7$.
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What is $|0|$?
What is $|0|$?
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- Absolute value of zero is always zero.
- Absolute value of zero is always zero.
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State the property: $|a \times b|$.
State the property: $|a \times b|$.
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$|a| \times |b|$. Absolute value of product equals product of absolute values.
$|a| \times |b|$. Absolute value of product equals product of absolute values.
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What is the inequality for 'at least 15'?
What is the inequality for 'at least 15'?
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$x \geq 15$. 'At least' means greater than or equal to.
$x \geq 15$. 'At least' means greater than or equal to.
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Solve for $x$: $|x + 2| \geq 3$.
Solve for $x$: $|x + 2| \geq 3$.
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$x \leq -5$ or $x \geq 1$. Distance from -2 is at least 3 units.
$x \leq -5$ or $x \geq 1$. Distance from -2 is at least 3 units.
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What is the solution to $x^2 \leq 16$?
What is the solution to $x^2 \leq 16$?
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$-4 \leq x \leq 4$. Take square root: $-4 \leq x \leq 4$.
$-4 \leq x \leq 4$. Take square root: $-4 \leq x \leq 4$.
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What is the solution to $x^2 > 9$?
What is the solution to $x^2 > 9$?
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$x > 3$ or $x < -3$. Take square root of both sides, considering both signs.
$x > 3$ or $x < -3$. Take square root of both sides, considering both signs.
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What does the inequality symbol $>$ mean?
What does the inequality symbol $>$ mean?
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Greater than. Symbol for strict greater than comparison.
Greater than. Symbol for strict greater than comparison.
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What inequality symbol represents 'greater than'?
What inequality symbol represents 'greater than'?
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$>$. Standard symbol for strict inequality.
$>$. Standard symbol for strict inequality.
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Solve for $x$: $x^2 - 4x < 0$.
Solve for $x$: $x^2 - 4x < 0$.
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$0 < x < 4$. Factor as $x(x-4) < 0$, find sign intervals.
$0 < x < 4$. Factor as $x(x-4) < 0$, find sign intervals.
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Find $x$ if $|3x + 4| = 7$.
Find $x$ if $|3x + 4| = 7$.
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$x = 1$ or $x = -\frac{11}{3}$. Set $3x + 4 = \pm 7$ and solve each equation.
$x = 1$ or $x = -\frac{11}{3}$. Set $3x + 4 = \pm 7$ and solve each equation.
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What is the solution set for $|x| < 4$?
What is the solution set for $|x| < 4$?
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$-4 < x < 4$. Distance from 0 is less than 4.
$-4 < x < 4$. Distance from 0 is less than 4.
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Describe the inequality $x > 5$.
Describe the inequality $x > 5$.
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All $x$ greater than 5. Open interval extending infinitely rightward.
All $x$ greater than 5. Open interval extending infinitely rightward.
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What is the solution to $-4 < x < 2$?
What is the solution to $-4 < x < 2$?
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All $x$ between -4 and 2. Compound inequality defines interval notation.
All $x$ between -4 and 2. Compound inequality defines interval notation.
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What is the graphical representation of $|x|$ on a number line?
What is the graphical representation of $|x|$ on a number line?
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Distance from 0. Absolute value measures distance from origin.
Distance from 0. Absolute value measures distance from origin.
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Solve for $x$: $|x - 3| = 5$.
Solve for $x$: $|x - 3| = 5$.
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$x = 8$ or $x = -2$. Distance from 3 equals 5, so $x-3 = \pm 5$.
$x = 8$ or $x = -2$. Distance from 3 equals 5, so $x-3 = \pm 5$.
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What does the inequality symbol $\leq$ mean?
What does the inequality symbol $\leq$ mean?
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Less than or equal to. Symbol combines less than with equality.
Less than or equal to. Symbol combines less than with equality.
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Solve the inequality: $2x + 3 > 7$.
Solve the inequality: $2x + 3 > 7$.
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$x > 2$. Subtract 3 from both sides, then divide by 2.
$x > 2$. Subtract 3 from both sides, then divide by 2.
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What is the absolute value of -7?
What is the absolute value of -7?
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- Absolute value converts negative numbers to positive.
- Absolute value converts negative numbers to positive.
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Solve for $x$: $|x - 4| < 2$.
Solve for $x$: $|x - 4| < 2$.
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$2 < x < 6$. Distance from 4 is less than 2 units.
$2 < x < 6$. Distance from 4 is less than 2 units.
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What does the inequality symbol $\geq$ mean?
What does the inequality symbol $\geq$ mean?
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Greater than or equal to. Symbol combines greater than with equality.
Greater than or equal to. Symbol combines greater than with equality.
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Solve for $x$: $3x - 4 \neq 5$.
Solve for $x$: $3x - 4 \neq 5$.
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$x \neq 3$. Solve $3x - 4 = 5$ gives $x = 3$, so $x \neq 3$.
$x \neq 3$. Solve $3x - 4 = 5$ gives $x = 3$, so $x \neq 3$.
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Solve the inequality: $-3x + 4 > 1$.
Solve the inequality: $-3x + 4 > 1$.
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$x < 1$. Rearrange to $-3x > -3$, then divide by -3.
$x < 1$. Rearrange to $-3x > -3$, then divide by -3.
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Solve for $x$: $2 < 3x + 1 \leq 8$.
Solve for $x$: $2 < 3x + 1 \leq 8$.
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$\frac{1}{3} < x \leq \frac{7}{3}$. Subtract 1, then divide by 3 for each part.
$\frac{1}{3} < x \leq \frac{7}{3}$. Subtract 1, then divide by 3 for each part.
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Solve for $x$: $|x + 7| > 4$.
Solve for $x$: $|x + 7| > 4$.
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$x > -3$ or $x < -11$. Distance from -7 exceeds 4 units.
$x > -3$ or $x < -11$. Distance from -7 exceeds 4 units.
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What is the absolute value of 0?
What is the absolute value of 0?
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- Zero has no sign, so absolute value is zero.
- Zero has no sign, so absolute value is zero.
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What is the solution set for $|x| = 0$?
What is the solution set for $|x| = 0$?
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$x = 0$. Only zero has absolute value of zero.
$x = 0$. Only zero has absolute value of zero.
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What is the solution to $|x| \geq 6$?
What is the solution to $|x| \geq 6$?
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$x \leq -6$ or $x \geq 6$. Distance from 0 is at least 6 units.
$x \leq -6$ or $x \geq 6$. Distance from 0 is at least 6 units.
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