Question

Solve the compound inequality 8x > –32 or 6x ≤ –48.

Answer 1

On the 8x > –32 first divide by the 8 from the both sides.

8x/8 as a fractions and it is greater than negative 32/8 as a fraction. And the equals to x is greater than negative 4.

On the 6x ≤ –48. Then divide by 6 from the both sides.

6x/6 as a fractions and it is less than negative 48/6 as a fraction. And the equals to x≤ negative 8.

Answer 2

(-∞,-8] U (-4,∞)

Explanation:

`8x > -32 \ or \ 6x\leq-48`

To solve the compound inequality we solve each inequality and combine the solutions

`8x > -32`

Divide both sides by 8

`x>-4`

`6x\leq-48`

Divide both sides by 6 to get x alone

`x\leq-8`

Now we combine both inequalities

`x>-4` or
`x\leq-8`

WE combine both inequalities

(-∞,-8] U (-4,∞)