Question

which number line shows the solution to the inequality?
-4x + 8 ≤ 20

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \(x\), we subtract 8 from both sides of the inequality \(-4x + 8 \leq 20\).
\[
-4x + 8 - 8 \leq 20 - 8
\]
Simplifying both sides gives:
\[
-4x \leq 12
\]

Step2: Divide by -4 (and reverse inequality)

When dividing an inequality by a negative number, the direction of the inequality sign reverses. We divide both sides by \(-4\):
\[
\frac{-4x}{-4} \geq \frac{12}{-4}
\]
Simplifying gives:
\[
x \geq -3
\]

Step3: Analyze the number line

The solution \(x \geq -3\) means we have a closed dot at \(-3\) (since the inequality is "greater than or equal to") and the line extends to the right (towards positive infinity). Looking at the options, the first number line has a closed dot at \(-3\) and extends to the right, which matches our solution.

Answer:

The first number line (with a closed dot at -3 and the green line extending to the right).