Question

How do you solve and graph `2/5a-4<2`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(4)` to each side of the inequality to isolate the `a` term while keeping the inequality balanced:

`2/5a - 4 + color(red)(4) < 2 + color(red)(4)`

`2/5a - 0 < 6`

`2/5a < 6`

Now, multiply each side of the inequality by `color(red)(5)/color(blue)(2)` to solve for `a` while keeping the inequality balanced:

`color(red)(5)/color(blue)(2) xx 2/5a < color(red)(5)/color(blue)(2) xx 6`

`cancel(color(red)(5))/cancel(color(blue)(2)) xx color(blue)(cancel(color(black)(2)))/color(red)(cancel(color(black)(5)))a < color(red)(5)/cancel(color(blue)(2)) xx color(blue)(cancel(color(black)(6)))3`

`a < 15`

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

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

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

graph{x < 15 [-20, 20, -10, 10]}