Question

How do you solve `-8x>24`?

Answer 1

See the entire solution process below:

Explanation:

Divide each side of the inequality by `color(blue)(-8)` to solve for `x` while keeping the inequality balanced. However, because we are multiplying or dividing by a negative term we must reverse the inequality:

`(-8x)/color(blue)(-8) color(red)(<) 24/color(blue)(-8)`

`(color(blue)(cancel(color(black)(-8)))x)/cancel(color(blue)(-8)) color(red)(<) -3`

`x < -3`

Answer 2

Just a slightly different approach plus demonstrating a very important fact about reversal of the inequality.

`x< -3`

Explanation:

Given:`" "-8x>24`

We wish to have the `x` value as positive so multiply both sides by `(-1)`

There is a trap in doing this: Multiply by negative 1 and you reverse the inequality.

Doing it incorrectly `-> 8x > -24color(red)(larr" this is very wrong")`
Doing it correctly `color(white)(.)->8x< -24color(green)( larr" correct way round")`

Divide both sides by 8

`8/8 x< -24/8`

But `" "8/8=1" and "24-:8=3`

`" "x < -3`