Question

-8x is less than or equal to 32
What is the inequalities that are possible.

Answer 1

We conclude that:

`-8x\le \:32\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}`

The solution graph on the number line is also attached.

Explanation:

Given the inequality

`-8x\:\le 32`

Solving the inequality

`-8x\:\le 32`

Multiply both sides by -1 (reverse the inequality)

`\left(-8x\right)\left(-1\right)\ge \:32\left(-1\right)`

Simplify

`8x\ge \:-32`

Divide both sides by 8

`(8x)/(8)\ge (-32)/(8)`

Simplify

`x\ge \:-4`

Therefore, we conclude that:

`-8x\le \:32\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-4\:\\ \:\mathrm{Interval\:Notation:}&\:[-4,\:\infty \:)\end{bmatrix}`

The solution graph on the number line is also attached.