Question

solve for ( x ) and graph the solution on the number line below.

( -24 leq -3x - 3 ) or ( -39 > -3x - 3 )

answer
attempt 1 out of 2

inequality notation:

number line:

number line with -12 to 12, arrows, and green circles near 0 and 2; note: touch line to delete. touch closed circle to change to open circle.

Explanation:

Step1: Solve first inequality

Start with $-24 \leq -3x - 3$.
Add 3 to both sides:
$-24 + 3 \leq -3x - 3 + 3$
$-21 \leq -3x$
Divide by -3 (reverse inequality):
$\frac{-21}{-3} \geq \frac{-3x}{-3}$
$7 \geq x$ or $x \leq 7$

Step2: Solve second inequality

Start with $-39 > -3x - 3$.
Add 3 to both sides:
$-39 + 3 > -3x - 3 + 3$
$-36 > -3x$
Divide by -3 (reverse inequality):
$\frac{-36}{-3} < \frac{-3x}{-3}$
$12 < x$ or $x > 12$

Answer:

Inequality Notation: $x \leq 7$ or $x > 12$

For the number line:

1. Place a closed circle at 7 and shade all values to the left of 7.
2. Place an open circle at 12 and shade all values to the right of 12.