Question

Which of the following is the correct graph of the solution to the inequality −18 > −5x + 2 ≥ −48?

(A) number line with a closed circle on 4 with shading to the left and an open circle on 10 with shading to the right

(B) number line with an open circle on 4 with shading to the left and a closed circle on 10 with shading to the right

(C) number line with a closed circle on 4 with shading to the right and an open circle on 10 with shading to the left

(D)number line with an open circle on 4 with shading to the right and a closed circle on 10 with shading to the left

Answer 1

Answer:

Option D. A number line with an open circle on 4 with shading to the right and a closed circle on 10 with shading to the left

Step-by-step explanation:

we have

$-18 > -5x+2 \geq -48$

Divide the compound inequality into two inequalities

$-5x+2 \geq -48$ -----> inequality A

$-5x \geq -48-2$

$-5x \geq -50$

Multiply by -1 both sides

$5x \leq 50$

Divide by 5 both sides

$x \leq 10$

The solution of inequality A is the interval ----> (-∞,10]

All real numbers less than or equal to 10

$-18 > -5x+2$ -----> inequality B

$-18-2 > -5x$

$-20 > -5x$

Multiply by -1 both sides

$20 < 5x$

Divide by 5 both sides

$4 < x$

Rewrite

$x > 4$

The solution of the inequality B is the interval ----> (4,∞)

All real numbers greater than 4

The solution of the compound inequality is

(-∞,10] ∩ (4,∞)= (4,10]

All real numbers greater than 4 and less than or equal to 10

A number line with an open circle on 4 with shading to the right and a closed circle on 10 with shading to the left

Answer 2

Answer:

D

Step-by-step explanation: