Question

solve the inequality and graph the solution.
10 + 3m ≤ 4
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
-5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 10 from both sides

To isolate the term with \( m \), we subtract 10 from both sides of the inequality \( 10 + 3m \leq 4 \).
\[
10 + 3m - 10 \leq 4 - 10
\]
Simplifying both sides, we get:
\[
3m \leq -6
\]

Step2: Divide both sides by 3

To solve for \( m \), we divide both sides of the inequality \( 3m \leq -6 \) by 3. Since 3 is a positive number, the direction of the inequality sign remains the same.
\[
\frac{3m}{3} \leq \frac{-6}{3}
\]
Simplifying both sides, we obtain:
\[
m \leq -2
\]

To graph the solution:

• The endpoint is at \( m = -2 \). Since the inequality is \( \leq \), we use a closed dot at \( -2 \).
• Then, we shade the number line to the left of \( -2 \) (because \( m \) is less than or equal to \( -2 \)).

Answer:

The solution to the inequality is \( m \leq -2 \). For the graph, plot a closed dot at \( -2 \) and shade to the left of \( -2 \) on the number line.