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

Question

.

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.