Question

solve for m and graph the solution. -2m - 3 ≥ 3 or 3m + 7 > 7 plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it. submit

Explanation:

Step1: Solve first inequality: isolate m

Start with $-2m - 3 \geq 3$. Add 3 to both sides:
$-2m - 3 + 3 \geq 3 + 3$
$-2m \geq 6$
Divide by -2 (reverse inequality):
$\frac{-2m}{-2} \leq \frac{6}{-2}$
$m \leq -3$

Step2: Solve second inequality: isolate m

Start with $3m + 7 > 7$. Subtract 7 from both sides:
$3m + 7 - 7 > 7 - 7$
$3m > 0$
Divide by 3:
$\frac{3m}{3} > \frac{0}{3}$
$m > 0$

Step3: Graph setup instructions

For $m \leq -3$: Plot a closed endpoint at $-3$, draw a ray extending left.
For $m > 0$: Plot an open endpoint at $0$, draw a ray extending right.

Answer:

The solution to the compound inequality is $m \leq -3$ or $m > 0$.

• On the number line:

1. Place a closed dot at $-3$ and draw a ray pointing left (towards $-4, -5, ...$).
2. Place an open dot at $0$ and draw a ray pointing right (towards positive numbers, though not shown on the given number line).