Question

Drag the tiles to the correct boxes to complete the pairs. Match each inequality to the number line that represents its solution. x – 99 ≤ -104 x – 51 ≤ -43 150 + x ≤ 144 75 < 69 – x

Answer 1

The four answers in the attached figure

Explanation:

Part 1) we have

`x-99\leq-104`

Solve for x

Adds 99 both sides

`x-99+99\leq-104+99`

`x\leq-5`

The solution is the interval ----> (-∞, -5]

All real numbers less than or equal to -5

In a number line, the shaded area at left of x=-5 (close circle)

Part 2) we have

`x-51\leq-43`

Solve for x

Adds 51 both sides

`x-51+51\leq-43+51`

`x\leq 8`

The solution is the interval ----> (-∞, 8]

All real numbers less than or equal to 8

In a number line, the shaded area at left of x=8 (close circle)

Part 3) we have

`150+x\leq144`

Solve for x

Subtract 150 both sides

`150+x-150\leq144-150`

`x\leq -6`

The solution is the interval ----> (-∞, -6]

All real numbers less than or equal to -6

In a number line, the shaded area at left of x=-6 (close circle)

Part 4) we have

`75<69-x`

Solve for x

Subtract 69 both sides

`75-69<69-x-69`

`6<-x`

Multiply by -1 both sides

`-6> x`

Rewrite

`x < -6`

The solution is the interval ----> (-∞, -6)

All real numbers less than -6

In a number line, the shaded area at left of x=-6 (open circle)