Question

How do you solve `−5x + 8 <= x − 4`?

Answer 1

`x >=2`

Explanation:

Isolate `x` on one side of the inequality, first by adding `-x` to both sides to get

`-5x + 8 - x <= color(red)(cancel(color(black)(x))) - color(red)(cancel(color(black)(x))) - 4`

`-6x + 8 <= -4`

Next, add `-8` to both sides of the inequality

`-6x + color(red)(cancel(color(black)(8))) - color(red)(cancel(color(black)(8))) <= -4 - 8`

`-6x <= -12`

FInally, divide both sides by `-6`, but do not forget that you need to change the sign of the inequality when you're multiplying or dividing by a negative number

`(color(red)(cancel(color(black)(-6)))x)/color(red)(cancel(color(black)(-6))) color(red)(>=) ((-12))/((-6))`

`x >= color(green)(2)`

So, for any value of `x` that is greater to or equal than `2`, your original inequality will be true.