Question

How do you solve and graph `5-2x>=27`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(5)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`5 - color(red)(5) - 2x >= 27 - color(red)(5)`

`0 - 2x >= 22`

`-2x >= 22`

Now, divide each side of the inequality by `color(blue)(-2)` to solve for `x` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`(-2x)/color(blue)(-2) color(red)(<=) 22/color(blue)(-2)`

`(color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(<=) -11`

`x <= -11`

To graph this we will draw a vertical line at `-11` 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 <= -11 [-20, 20, -10, 10]}