Question

How do you solve and graph `r-8<=7`?

Answer 1

See a solution process below:

Explanation:

Add `color(red)(8)` to each side of the inequality to solve for `r` while keeping the inequality balanced:

`r - 8 + color(red)(8) <= 7 + color(red)(8)`

`r - 0 <= 15`

`r <= 15`

To graph this we will draw a vertical line at `15` on the horizontal axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade to the left side of the line because the inequality operator also contains a "less than" clause:

graph{x <= 15 [-30, 30, -15, 15]}

Answer 2

Given: `r - 8 <= 7`

Add 8 to both sides:

`r <= 15`

On polar graph paper, draw a circle, centered at the origin, with radius 15 and then shade the inside of the circle to indicate that every point within the circle and on the edge is included.

Here is a graph of the inequality: