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

Number lines Inequality

First ⇔
`(x)/(4)\leq(-3)/(2)`

Second ⇔
`(-75x)/(4)>(225)/(2)`

Third ⇔
`(2x)/(3)>(-16)/(3)`

Fourth ⇔
`(7x)/(9)>(-14)/(3)`

Explanation:

Inequality 1.
`(7x)/(9)>(-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.
`(-75x)/(4)>(225)/(2)`

Multiply both sides by 4 , we get

`-75x>450`

Divide both sides by -6, we get

`x<-6` which is shown by the second number line.

Inequality 3.
`(x)/(4)\leq(-3)/(2)`

Multiply both sides by 4 , we get

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

Inequality 2.
`(2x)/(3)>(-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.