Question

How do you solve and graph `4x-3<2x`?

Answer 1

`x < 3/2`

Explanation:

You can solve this inequality by isolating `x` on one side.

This can be done in three steps. First, add `3` to both sides of the inequality to get

`4x - color(red)(cancel(color(black)(3))) + color(red)(cancel(color(black)(3))) < 2x + 3`

`4x < 2x + 3`

Now add `-2x` to both sides of the inequality

`4x - 2x < color(red)(cancel(color(black)(2x))) - color(red)(cancel(color(black)(2x))) + 3`

`2x < 3`

Finally, divide both sides of the inequality by `2` to isolate `x`

`(color(red)(cancel(color(black)(2)))x)/color(red)(cancel(color(black)(2))) < 3/2`

`x < color(green)(3/2)`

To graph the solution set for this inequality, draw a dotted vertical line parallel to the `y`-axis that goes through `x=3/2`.

Since you want all the `x` values that are smaller than `3/2`, shade the region to the left of `x=3/2`.

The dotted line signifies that `x=3/2` is not a part of the solution set.

graph{x<3/2 [-10, 10, -5, 5]}