Question

How do you graph the solution of `-3( r - 4) \geq 0` on a number line?

Answer 1

See a solution process below:

Explanation:

Before we graph the inequality we must first solve it for `r`. First, divide each side of the inequality by `color(blue)(-3)` to eliminate the need for the parenthesis. However, because we are multiplying or dividing an inequality by a negative number we must reverse he inequality operator.

`(-3(r - 4))/color(blue)(-3) color(red)(<=) 0/color(blue)(-3)`

`(color(blue)(cancel(color(black)(-3)))(r - 4))/cancel(color(blue)(-3)) color(red)(<=) 0`

`r - 4 color(red)(<=) 0`

Now, add `color(blue)(4)` to each side of the inequality to solve for `r` while keeping the inequality balanced:

`r - 4 + color(blue)(4) color(red)(<=) 0 + color(blue)(4)`

`r - 0 color(red)(<=) 4`

`r <= 4`

To graph this we will draw a vertical line at `4` 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 <= 4 [-10, 10, -5, 5]}