Solve |2x - 6| > 10{x|-2 < x < 8}{x|x < -2 or x > 8}{x|x < -8 or x > 2}

To solve the inequality |2x - 6| > 10, we need to consider different cases based on the value of x.

Case 1: -2 < x < 8 In this case, the absolute value |2x - 6| can be written as 2x - 6 since 2x - 6 is positive for all x in this range. Therefore, the inequality becomes 2x - 6 > 10.

Solving this inequality, we add 6 to both sides: 2x - 6 + 6 > 10 + 6 2x > 16

Dividing both sides by 2: x > 8

So, for -2 < x < 8, the solution is x > 8.

Case 2: x < -2 or x > 8 In this case, the absolute value |2x - 6| can be written as -(2x - 6) since 2x - 6 is negative for x < -2 or x > 8. Therefore, the inequality becomes -(2x - 6) > 10.

Solving this inequality, we multiply both sides by -1, which changes the direction of the inequality: 2x - 6 < -10

Adding 6 to both sides: 2x - 6 + 6 < -10 + 6 2x < -4

Dividing both sides by 2: x < -2

So, for x < -2 or x > 8, the solution is x < -2.

Case 3: x < -8 or x > 2 In this case, the absolute value |2x - 6| can be written as -(2x - 6) since 2x - 6 is negative for x < -8 or x > 2. Therefore, the inequality becomes -(2x - 6) > 10.

Solving this inequality, we multiply both sides by -1, which changes the direction of the inequality: 2x - 6 < -10

Adding 6 to both sides: 2x - 6 + 6 < -10 + 6 2x < -4

Dividing both sides by 2: x < -2

So, for x < -8 or x > 2, the solution is x < -2.

In summary, the solution to the inequality |2x - 6| > 10 is: x > 8 for -2 < x < 8 x < -2 for x < -2 or x > 8 x < -2 for x < -8 or x > 2