Question

How do you graph the inequality `14x-12> -31` on the coordinate plane?

Answer 1

See a solution process below:

Explanation:

First, we need to solve for `x`. Add `color(red)(12)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`14x - 12 + color(red)(12) > -31 + color(red)(12)`

`14x - 0 > -19`

`14x > -19`

Now, divide each side of the inequality by `color(red)(14)` to solve for `x` while keeping the inequality balanced:

`(14x)/color(red)(14) > -19/color(red)(14)`

`(color(red)(cancel(color(black)(14)))x)/cancel(color(red)(14)) > -19/14`

`x > -19/14`

To graph this we will draw a vertical line at `-19/14` on the horizontal axis.

The line will be a dahsed line because the inequality operator does not contain an "or equal to" clause so the line is not part of the solution set.

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

graph{x> -19/14 [-5, 5, -2.5, 2.50]}