Question

How do you solve and graph `7x-12<8`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(12)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`7x - 12 + color(red)(12) < 8 + color(red)(12)`

`7x - 0 < 20`

`7x < 20`

Now, divide each side of the inequality by `color(red)(7)` to solve for `x` while keeping the inequality balanced:

`(7x)/color(red)(7) < 20/color(red)(7)`

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) < 20/7`

`x < 20/7`

Or

`x < 2.857` rounded to the nearest thousandth.

To graph this we will draw a vertical line at `20/7` on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

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

graph{x < 20/7 [-10, 10, -5, 5]}