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

Answer:

The four answers in the attached figure

Step-by-step 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

$75$

Solve for x

Subtract 69 both sides

$75-69$

$6$

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)