Question

use the number line to represent the solution to $120x + 180 \leq 1,020$. select the ray. move the point on the ray to the correct place on the number line.

Explanation:

Step1: Subtract 180 from both sides

To isolate the term with \( x \), we subtract 180 from both sides of the inequality \( 120x + 180 \leq 1020 \).
\[
120x + 180 - 180 \leq 1020 - 180
\]
\[
120x \leq 840
\]

Step2: Divide both sides by 120

To solve for \( x \), we divide both sides of the inequality \( 120x \leq 840 \) by 120.
\[
\frac{120x}{120} \leq \frac{840}{120}
\]
\[
x \leq 7
\]

Answer:

The solution to the inequality \( 120x + 180 \leq 1020 \) is \( x \leq 7 \). On the number line, we would select the ray that points to the left (since \( x \) is less than or equal to 7) with a closed dot at 7 (because the inequality is "less than or equal to").