Question

solve for $x$ and graph the solution on the number line below.$-13 \leq -x - 7$ or $-16 \geq -x - 7$answer attempt 1 out of 2$<$ $>$ $\leq$ $\geq$ orinequality notation:number line:click and drag to plot line.

Explanation:

Step1: Solve first inequality

Start with $-13 \leq -x - 7$
Add 7 to both sides:
$-13 + 7 \leq -x$
$\implies -6 \leq -x$
Multiply by -1 (reverse inequality):
$6 \geq x$ or $x \leq 6$

Step2: Solve second inequality

Start with $-16 \geq -x - 7$
Add 7 to both sides:
$-16 + 7 \geq -x$
$\implies -9 \geq -x$
Multiply by -1 (reverse inequality):
$9 \leq x$ or $x \geq 9$

Step3: Combine solutions

The combined solution is $x \leq 6$ or $x \geq 9$

Step4: Number Line Graph Instructions

1. Place a closed circle at $6$ and shade all values to the left (towards negative infinity).
2. Place a closed circle at $9$ and shade all values to the right (towards positive infinity).

Answer:

$x \leq 6$ or $x \geq 9$