Question

Solve |2x - 6| > 10

x
x
-2 < x < 8

Answer 1

x

Explanation:

|2x - 6| > 10

We split the inequality into two functions, one positive and one negative. The negative one flips the inequality. since this is greater than, this is an or problem

2x-6 >10 or 2x-6 < -10

Add 6 to each side

2x-6+6 > 10+6 2x-6+6 < -10+6

2x > 16 2x < -4

Divide by 2

2x/2 > 16/2 2x/2 < -4/2

x >8 or x < -2

Answer 2

x < -2 or x > 8

EXPLANATION

The given absolute inequality is

`|2x - 6| \: > \: 10`

By the definition of absolute value,

`(2x - 6)\: > \: 10 \: or \: \: - (2x - 6)\: > \: 10`

Multiply through the second inequality by -1 and reverse the inequality sign

`2x - 6\: > \: 10 \: or \: \: 2x - 6\: < \: - 10`

`2x \: > \: 10 + 6\: or \: \: 2x \: < \: - 10 + 6`

Simplify

`2x \: > \: 16\: or \: \: 2x \: < \: -4`

Divide through by 2

`x \: > \: 8\: or \: \: x \: < \: -2`