Question

solve for x and graph the solution on the number line below.
-36 < -3x - 9 or -42 ≥ -3x - 9
answer attempt 1 out of 2
inequality notation:
number line:

Explanation:

Step1: Solve first inequality

Start with $-36 < -3x - 9$.
Add 9 to both sides:
$-36 + 9 < -3x - 9 + 9$
$-27 < -3x$
Divide by -3 (reverse inequality):
$\frac{-27}{-3} > \frac{-3x}{-3}$
$9 > x$ or $x < 9$

Step2: Solve second inequality

Start with $-42 \geq -3x - 9$.
Add 9 to both sides:
$-42 + 9 \geq -3x - 9 + 9$
$-33 \geq -3x$
Divide by -3 (reverse inequality):
$\frac{-33}{-3} \leq \frac{-3x}{-3}$
$11 \leq x$ or $x \geq 11$

Step3: Combine solutions

The compound inequality uses "or", so combine the two results.

Answer:

Inequality Notation:

$x < 9$ or $x \geq 11$

Number Line Graph Instructions:

1. For $x < 9$: Draw an open circle at 9, then draw an arrow pointing left from the circle to cover all values less than 9.
2. For $x \geq 11$: Draw a closed circle at 11, then draw an arrow pointing right from the circle to cover all values greater than or equal to 11.