Question

How do you solve the inequality `5x < 2x - 6`?

Answer 1

`color(green)(x < -2)`

Explanation:

Remember that given an inequality:
[1]`color(white)("XXX")` you can add or subtract the same amount to/from both sides, and
[2]`color(white)("XXX")` you can multiply or divide both sides by any positive amount
without changing the validity or direction of the inequality.

Given:
`color(white)("XXX")color(green)(5x < 2x-6)`

We can subtract `color(green)(2x)` from both sides to get:
`color(white)("XXX")color(green)(3x < -6)`

Then, if we divide both sides by `color(green)3`
`color(white)("XXX")color(green)(x < -2)`