Question

Match the inequality to the number line that represents its solution

Answer 1

Tile 1 goes to graph D
Tile 2 goes to graph B
Tile 3 goes to graph A
Tile 4 goes to graph C

Desmos graphing calculator at desmos.com/calculator is a great tool.

Answer 2

Answer:    

Number lines                             Inequality

First                   ⇔              $\dfrac{x}{4}\leq\dfrac{-3}{2}$

Second             ⇔              $\dfrac{-75x}{4}>\dfrac{225}{2}$

Third                 ⇔              $\dfrac{2x}{3}>\dfrac{-16}{3}$

Fourth              ⇔              $\dfrac{7x}{9}>\dfrac{-14}{3}$

Step-by-step explanation:

Inequality 1. $\dfrac{7x}{9}>\dfrac{-14}{3}$

Multiply both sides by 9 , we get

$7x>-42$

Divide both sides by 7, we get

$x>-6$ which is shown by the fourth number line.

Inequality 2. $\dfrac{-75x}{4}>\dfrac{225}{2}$

Multiply both sides by 4 , we get

$-75x>450$

Divide both sides by -6, we get

$x$ which is shown by the second number line.

Inequality 3. $\dfrac{x}{4}\leq\dfrac{-3}{2}$

Multiply both sides by 4 , we get

$x\leq-6$ which is shown by the first number line.

Inequality 2. $\dfrac{2x}{3}>\dfrac{-16}{3}$

Multiply both sides by 3 , we get

$2x>-16$

Divide both sides by 2, we get

$x>8$ which is shown by the third number line.