Linear Inequalities - SAT Math
Card 1 of 37
Solve $5 - 2x \neq 13$ for $x$.
Solve $5 - 2x \neq 13$ for $x$.
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$x \neq -4$. Subtract 5, divide by -2 to get $x = -4$.
$x \neq -4$. Subtract 5, divide by -2 to get $x = -4$.
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How do you graph $x \leq -2$ on a number line?
How do you graph $x \leq -2$ on a number line?
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Closed circle at -2, arrow to the left. Closed circle includes -2 in the solution set.
Closed circle at -2, arrow to the left. Closed circle includes -2 in the solution set.
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Solve $x - 5 \geq 0$ for $x$.
Solve $x - 5 \geq 0$ for $x$.
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$x \geq 5$. Add 5 to both sides to isolate $x$.
$x \geq 5$. Add 5 to both sides to isolate $x$.
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What is the solution to $4x + 8 < 16$?
What is the solution to $4x + 8 < 16$?
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$x < 2$. Subtract 8, divide by 4 to solve inequality.
$x < 2$. Subtract 8, divide by 4 to solve inequality.
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Solve $-3(x + 4) \neq 9$ for $x$.
Solve $-3(x + 4) \neq 9$ for $x$.
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$x \neq -7$. Distribute -3, subtract 12, divide by -3.
$x \neq -7$. Distribute -3, subtract 12, divide by -3.
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Solve $2x + 3 \leq 7$ for $x$.
Solve $2x + 3 \leq 7$ for $x$.
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$x \leq 2$. Subtract 3, divide by 2 to solve inequality.
$x \leq 2$. Subtract 3, divide by 2 to solve inequality.
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What is the inequality for 'x is at least 5'?
What is the inequality for 'x is at least 5'?
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$x \geq 5$. 'At least' means greater than or equal to.
$x \geq 5$. 'At least' means greater than or equal to.
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Solve $-4x + 5 \neq -11$ for $x$.
Solve $-4x + 5 \neq -11$ for $x$.
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$x \neq 4$. Add 11, divide by -4 to get $x = 4$.
$x \neq 4$. Add 11, divide by -4 to get $x = 4$.
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How do you graph $x > 3$ on a number line?
How do you graph $x > 3$ on a number line?
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Open circle at 3, arrow to the right. Open circle shows 3 is not included.
Open circle at 3, arrow to the right. Open circle shows 3 is not included.
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What is the inequality for 'x is more than 10'?
What is the inequality for 'x is more than 10'?
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$x > 10$. 'More than' means strictly greater than.
$x > 10$. 'More than' means strictly greater than.
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What is the solution set for $5x + 2 \neq 12$?
What is the solution set for $5x + 2 \neq 12$?
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$x \neq 2$. Subtract 2, divide by 5 to find excluded value.
$x \neq 2$. Subtract 2, divide by 5 to find excluded value.
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What inequality symbol represents 'greater than or equal to'?
What inequality symbol represents 'greater than or equal to'?
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$\geq$. Combines greater than and equal to in one symbol.
$\geq$. Combines greater than and equal to in one symbol.
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What is the inequality representation of 'p is at most 4'?
What is the inequality representation of 'p is at most 4'?
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$p \leq 4$. 'At most' means less than or equal to.
$p \leq 4$. 'At most' means less than or equal to.
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What is the solution set for $3(x - 4) < 6$?
What is the solution set for $3(x - 4) < 6$?
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$x < 6$. Distribute 3, add 12, then divide by 3.
$x < 6$. Distribute 3, add 12, then divide by 3.
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Solve $8 - x \neq 5$ for $x$.
Solve $8 - x \neq 5$ for $x$.
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$x \neq 3$. Solve $x = 3$ from the equation $8 - x = 5$.
$x \neq 3$. Solve $x = 3$ from the equation $8 - x = 5$.
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Solve $0 < 2x + 4$ for $x$.
Solve $0 < 2x + 4$ for $x$.
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$x > -2$. Subtract 4, divide by 2 to solve inequality.
$x > -2$. Subtract 4, divide by 2 to solve inequality.
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Solve $-5x \neq 10$ for $x$.
Solve $-5x \neq 10$ for $x$.
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$x \neq -2$. Divide both sides by -5 to isolate $x$.
$x \neq -2$. Divide both sides by -5 to isolate $x$.
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Solve $4 - 2x \neq 0$ for $x$.
Solve $4 - 2x \neq 0$ for $x$.
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$x \neq 2$. Solve $2x = 4$ to find the excluded value.
$x \neq 2$. Solve $2x = 4$ to find the excluded value.
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What inequality symbol represents 'less than or equal to'?
What inequality symbol represents 'less than or equal to'?
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$\leq$. Combines less than and equal to in one symbol.
$\leq$. Combines less than and equal to in one symbol.
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Solve $-3x + 7 \neq 1$ for $x$.
Solve $-3x + 7 \neq 1$ for $x$.
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$x \neq 2$. Subtract 7, divide by -3 to get $x = 2$.
$x \neq 2$. Subtract 7, divide by -3 to get $x = 2$.
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Solve the inequality $-2x + 9 < 3$ for $x$.
Solve the inequality $-2x + 9 < 3$ for $x$.
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$x > 3$. Subtract 9, divide by -2, flip inequality sign.
$x > 3$. Subtract 9, divide by -2, flip inequality sign.
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What does the inequality $x < 0$ represent?
What does the inequality $x < 0$ represent?
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Negative numbers. All values to the left of zero on number line.
Negative numbers. All values to the left of zero on number line.
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Solve $6(x - 2) > 12$ for $x$.
Solve $6(x - 2) > 12$ for $x$.
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$x > 4$. Distribute 6, add 12, then divide by 6.
$x > 4$. Distribute 6, add 12, then divide by 6.
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What is the solution to $x/3 \neq 2$?
What is the solution to $x/3 \neq 2$?
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$x \neq 6$. Multiply both sides by 3 to isolate $x$.
$x \neq 6$. Multiply both sides by 3 to isolate $x$.
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Identify the inequality symbol for 'greater than'.
Identify the inequality symbol for 'greater than'.
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$>$. Symbol for strict inequality without equality.
$>$. Symbol for strict inequality without equality.
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Solve $3x + 7 \leq 16$ for $x$.
Solve $3x + 7 \leq 16$ for $x$.
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$x \leq 3$. Subtract 7, divide by 3 to isolate $x$.
$x \leq 3$. Subtract 7, divide by 3 to isolate $x$.
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What is the inequality for 'y is less than 8'?
What is the inequality for 'y is less than 8'?
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$y < 8$. 'Less than' means strictly smaller than 8.
$y < 8$. 'Less than' means strictly smaller than 8.
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What is the solution to $x + 3 > 10$?
What is the solution to $x + 3 > 10$?
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$x > 7$. Subtract 3 from both sides to isolate $x$.
$x > 7$. Subtract 3 from both sides to isolate $x$.
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Solve $7x - 3 \neq 25$ for $x$.
Solve $7x - 3 \neq 25$ for $x$.
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$x \neq 4$. Add 3, divide by 7 to find excluded value.
$x \neq 4$. Add 3, divide by 7 to find excluded value.
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What is the solution to the inequality $2x + 3 > 7$?
What is the solution to 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 solution to the inequality $-3x \neq 9$?
What is the solution to the inequality $-3x \neq 9$?
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$x \neq -3$. Divide both sides by $-3$, keeping the not-equal sign.
$x \neq -3$. Divide both sides by $-3$, keeping the not-equal sign.
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Solve the inequality: $5x - 4 \text{ } \text{≤} \text{ } 11$.
Solve the inequality: $5x - 4 \text{ } \text{≤} \text{ } 11$.
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$x \text{ } \text{≤} \text{ } 3$. Add 4 to both sides, then divide by 5.
$x \text{ } \text{≤} \text{ } 3$. Add 4 to both sides, then divide by 5.
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What is the solution to $4 - x > 8$?
What is the solution to $4 - x > 8$?
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$x < -4$. Subtract 4 from both sides, then divide by $-1$ and flip sign.
$x < -4$. Subtract 4 from both sides, then divide by $-1$ and flip sign.
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What does the inequality $x \text{ } \text{≤} \text{ } 0$ indicate about $x$?
What does the inequality $x \text{ } \text{≤} \text{ } 0$ indicate about $x$?
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$x$ is less than or equal to zero. The variable can be zero or any negative value.
$x$ is less than or equal to zero. The variable can be zero or any negative value.
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Solve the inequality: $-2y + 5 \text{ } \text{≥} \text{ } 11$.
Solve the inequality: $-2y + 5 \text{ } \text{≥} \text{ } 11$.
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$y \text{ } \text{≤} \text{ } -3$. Subtract 5, divide by $-2$, and flip the inequality sign.
$y \text{ } \text{≤} \text{ } -3$. Subtract 5, divide by $-2$, and flip the inequality sign.
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State the rule for reversing an inequality sign.
State the rule for reversing an inequality sign.
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Multiply or divide both sides by a negative number. This operation changes the direction of the inequality.
Multiply or divide both sides by a negative number. This operation changes the direction of the inequality.
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What is the solution to $3(x - 2) < 6$?
What is the solution to $3(x - 2) < 6$?
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$x < 4$. Distribute 3, add 6 to both sides, then divide by 3.
$x < 4$. Distribute 3, add 6 to both sides, then divide by 3.
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