Question

PLEASE HELP!! solve |2x-2| ≥6.

Answer 1

Answer:

x ≤ -2    OR  x ≥ 4

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Step-by-step explanation:

We are given the inequality:

|2x - 2| ≥ 6

Getting rid of the Modulus:

Since 2x-2 is in modulus:

|2x-2| =  -(2x-2)    OR   2x-2

(since the modulus of both these values is 2x-2)

Hence, our inequality can be written in 2 different ways:

1. 2x-2 ≥ 6                              (if 2x-2 ≥ 1)
2. -(2x - 2) ≥ 6                         (if 2x-2 < 0)

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Solving these 2 inequalities:

Solving inequality 1:

2x - 2 ≥ 6                

2x ≥ 8                     [adding 2 on both sides]

x ≥ 4                       [dividing both the sides by 2]

This is the solution of the inequality if: 2x-2 ≥ 0

Solving Inequality 2:

-(2x-2) ≥ 6

It can be rewritten as:

2 - 2x ≥ 6                

2 ≥ 6 + 2x                [adding 2x on both the sides]  

-4 ≥ 2x                     [Subtracting 6 from both sides]

x ≤ -2                       [Dividing both sides by 2]

This is the solution of the given inequality if: 2x-2 < 0

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Solution of the given Inequality:

Therefore, the solution of the given inequality |2x-2| ≥ 6 are:

x ≥ 4   (if 2x-2 ≥ 0)

x ≤ -2  (if 2x-2 < 0)

Hence, option C is correct!