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

ANSWER

{x|x < -2 or x > 8}

EXPLANATION

The given absolute inequality is

By the definition of absolute value,

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

Simplify

Divide through by 2

{x|x < -2 or x > 8}

Step-by-step 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

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