Question

Use the number line to represent the solution to 120x+180less than or equal to 1,020
.

Select the ray. Move the point on the ray to the correct place on the number line.

Answer 1

To solve the inequality \( 120x + 180 \leq 1,020 \), we first isolate \( x \).

1. Subtract 180 from both sides:
\[
120x \leq 1,020 - 180
\]
\[
120x \leq 840
\]

2. Divide both sides by 120:
\[
x \leq \frac{840}{120}
\]
\[
x \leq 7
\]

The solution \( x \leq 7 \) means that \( x \) can take any value from negative infinity up to and including 7.

To represent this solution on a number line:
- Draw a number line.
- Indicate the point 7 on the number line.
- Use a closed circle (or point) to represent that 7 is included in the solution (since it is "less than or equal to").
- Shade the region to the left of 7 to show all values less than or equal to 7.

So, you'll have a closed circle at 7 and a shaded ray extending leftwards towards negative infinity.

If you have a specific number line interface or app to use, you would place the point at 7 with a closed circle and adjust the shading accordingly.