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ANSWER

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

EXPLANATION

The given absolute inequality is

[tex] |2x - 6| \: > \: 10[/tex]

By the definition of absolute value,

[tex] (2x - 6)\: > \: 10 \: or \: \: - (2x - 6)\: > \: 10[/tex]

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

[tex]2x - 6\: > \: 10 \: or \: \: 2x - 6\: < \: - 10[/tex]

[tex]2x \: > \: 10 + 6\: or \: \: 2x \: < \: - 10 + 6[/tex]

Simplify

[tex]2x \: > \: 16\: or \: \: 2x \: < \: -4[/tex]

Divide through by 2

[tex]x \: > \: 8\: or \: \: x \: < \: -2[/tex]

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Answer:

{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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