Question

How do you solve `-2x + 8\leq 24`?

Answer 1

`x >= -8`

Explanation:

`-2x + 8 <= 24`

Subtract `color(blue)8` from both sides:
`-2x + 8 quadcolor(blue)(-quad8) <= 24 quadcolor(blue)(-quad8)`

`-2x <= 16`

Now we have to divide both sides by `-2`. However, in inequalities, when you multiply or divide both sides by a negative number, you have to switch the inequality sign. So the `<=` becomes `>=`:
`(-2x)/color(blue)(-2) color(blue)(>=) 16/color(blue)(-2)`

Therefore,
`x >= -8`

Hope this helps!