Question

Select the graph that would represent the best presentation of the solution set.

|2x - 6| > 10

Answer 1

|2x + 6| > 10
(2x + 6) > 10 -(2x + 6) > 10
2x + 6 > 10 -2x - 6 > 10
- 6 - 6 + 6 + 6
2x > 4 -2x > 16
2 2 -2 -2
x > 2 x > -8

Answer 2

-2 > x > 8

Explanation:

given that,

|2 x - 6| > 10

mod means the value will be positive when mod is solved.

it can be written as

± (2 x - 6) > 10

i) (2 x - 6) > 10

2 x > 16

x > 8

ii) -(2 x - 6) > 10

-2 x +6 > 10

- x > 2

x < -2

hence , -2 > x > 8

Shaded portion shows the required area.