Linear Inequalities - SAT Math

The solution set is $x > 2$. Subtract 5 from both sides, then divide by 2.

$x < 4$. Distribute 3, add 6 to both sides, then divide by 3.

$x > 2$. Subtract 3 from both sides, then divide by 2.

$4 \leq x$. Reverses the typical order to show 4 as the lesser value.

$x < 3$. Move $2x$ left and $-3$ right, then divide by 3.

$x < -4$. Subtract 4 from both sides, then divide by $-1$ and flip sign.

$y \text{ } \text{≤} \text{ } -3$. Subtract 5, divide by $-2$, and flip the inequality sign.

$x \leq 7$. 'At most' means less than or equal to.

Multiply or divide both sides by a negative number. This operation changes the direction of the inequality.

$\geq$. Standard mathematical symbol for greater than or equal to.

No, $x = -1$ does not satisfy $2x + 3 > 0$. Substituting gives $2(-1) + 3 = 1 > 0$ is false.

$x < 10$. Standard notation for values below 10.

$x \neq -3$. Divide both sides by $-3$, keeping the not-equal sign.

$x \text{ } \text{≤} \text{ } 3$. Add 4 to both sides, then divide by 5.

$x \geq 5$. Distribute 3, add 6 to both sides, then divide by 3.

A horizontal line at $y = 4$ with a dashed line. Uses dashed line since $\neq$ excludes the boundary value.

$x \leq 3$. Subtract 7, divide by 3 to isolate $x$.

$y < 8$. 'Less than' means strictly smaller than 8.

$x > 7$. Subtract 3 from both sides to isolate $x$.

$x \neq 4$. Add 3, divide by 7 to find excluded value.

Closed circle at -2, arrow to the left. Closed circle includes -2 in the solution set.

$x \geq 5$. Add 5 to both sides to isolate $x$.

$x < 2$. Subtract 8, divide by 4 to solve inequality.

$x \neq -7$. Distribute -3, subtract 12, divide by -3.

$x \leq 2$. Subtract 3, divide by 2 to solve inequality.

$x \neq 4$. Add 11, divide by -4 to get $x = 4$.

Open circle at 3, arrow to the right. Open circle shows 3 is not included.

$x \neq -4$. Subtract 5, divide by -2 to get $x = -4$.

$x \geq 5$. 'At least' means greater than or equal to.

$x > 10$. 'More than' means strictly greater than.

$x \neq 2$. Subtract 2, divide by 5 to find excluded value.

$\geq$. Combines greater than and equal to in one symbol.

$p \leq 4$. 'At most' means less than or equal to.

$x < 6$. Distribute 3, add 12, then divide by 3.

$x \neq 3$. Solve $x = 3$ from the equation $8 - x = 5$.

$x > -2$. Subtract 4, divide by 2 to solve inequality.

$x \neq -2$. Divide both sides by -5 to isolate $x$.

$x \neq 2$. Solve $2x = 4$ to find the excluded value.

$\leq$. Combines less than and equal to in one symbol.

$x \neq 2$. Subtract 7, divide by -3 to get $x = 2$.

$x > 3$. Subtract 9, divide by -2, flip inequality sign.

Negative numbers. All values to the left of zero on number line.

$x > 4$. Distribute 6, add 12, then divide by 6.

$x \neq 6$. Multiply both sides by 3 to isolate $x$.

$>$. Symbol for strict inequality without equality.

$x < 4$. Distribute 3, add 6 to both sides, then divide by 3.

Multiply or divide both sides by a negative number. This operation changes the direction of the inequality.

$y \text{ } \text{≤} \text{ } -3$. Subtract 5, divide by $-2$, and flip the inequality sign.

$x$ is less than or equal to zero. The variable can be zero or any negative value.

$x < -4$. Subtract 4 from both sides, then divide by $-1$ and flip sign.

$x \text{ } \text{≤} \text{ } 3$. Add 4 to both sides, then divide by 5.

$x \neq -3$. Divide both sides by $-3$, keeping the not-equal sign.

$x > 2$. Subtract 3 from both sides, then divide by 2.