Question

Solve for x.

5x – 10 > 20 or 5x – 10 ≤ –15

A. –5 ≤ x < 6
B. –1 ≤ x < 6
C. x ≤ –5 or x > 6
D. x ≤ –1 or x > 6

Answer 1

`\text{The solution is }x \leq -1\text{ or }x > 6`

Explanation:

Given the two inequalities

`5x - 10 > 20\text{ or }5x - 10 \leq -15`

we have to solve the above two for x.

`5x - 10 > 20`

Adding 10 on both sides

`5x>20+10`

`5x>30`

Divide throughout by 5, we get

`x>(30)/(5)=6`

`\text{second inequality:}\thinspace 5x - 10 \leq -15`

`5x - 10 \leq -15`

Adding 10 on both sides

`5x \leq -15+10`

`5x\leq -5`

`x \leq -1`

hence, the solution is

`x \leq -1\text{ or }x > 6`

which is required solution.

Option D is correct.

Answer 2

I'm going to go with letter D.