Question

solve for x and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (∅), leave the number line blank.

5 ≥ -5x - 10 or -65 ≤ -5x - 10

answer attempt 1 out of a

inequality notation:

number line:

Explanation:

Step1: Solve first inequality

Start with $5 \geq -5x - 10$.
Add 10 to both sides:
$5 + 10 \geq -5x - 10 + 10$
$15 \geq -5x$
Divide by -5 (reverse inequality):
$\frac{15}{-5} \leq \frac{-5x}{-5}$
$-3 \leq x$ or $x \geq -3$

Step2: Solve second inequality

Start with $-65 \leq -5x - 10$.
Add 10 to both sides:
$-65 + 10 \leq -5x - 10 + 10$
$-55 \leq -5x$
Divide by -5 (reverse inequality):
$\frac{-55}{-5} \geq \frac{-5x}{-5}$
$11 \geq x$ or $x \leq 11$

Step3: Combine the solutions

The compound inequality is "or", so combine $x \geq -3$ and $x \leq 11$. This covers all real numbers between -3 and 11, inclusive.

Answer:

Inequality Notation: $-3 \leq x \leq 11$

For the number line: Draw a closed dot at $-3$ and a closed dot at $11$, then shade the region between these two points.