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Bingel [31]
3 years ago
9

Solve |2x - 6| > 10

Mathematics
2 answers:
Likurg_2 [28]3 years ago
8 0

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

inn [45]3 years ago
7 0

ANSWER

{x|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

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