SOLUTION: Can you help me solve this equation: 2|x+4|-2=8

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Question 1132528: Can you help me solve this equation: 2|x+4|-2=8

Found 3 solutions by josgarithmetic, MathLover1, ikleyn:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for the absolute value function first.
2abs%28x%2B4%29=8%2B2=10
abs%28x%2B4%29=5

If what's inside is positive or 0, then
x%2B4=5
x=1

If what's inside is negative, then
-x-4=5
-x=9
x=-9

SOLUTION:
system%28x=-9%2Cor%2Cx=1%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2abs%28x%2B4%29-2=8
2abs%28x%2B4%29=8%2B2
2abs%28x%2B4%29=10
abs%28x%2B4%29=10%2F2
abs%28x%2B4%29=5
sqrt%28%28x%2B4%29%29%5E2=5

solutions:
x%2B4=5=>x=5-4=>x=1
-%28x%2B4%29=5=>-x-4=5=>-5-4=x=>x=-9

+graph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+10%2C+2abs%28x%2B4%29-2%2C+8%29+

Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.

2*|x+4| - 2 = 8  ====>  (move -2 to the right, changing the sign)  ====>


2*|x+4| = 8 + 2 = 10   ====>  (divide both sides by 2)  ====>


|x+4| = 10%2F2 = 5


At this point you have two alternatives.


    
    EITHER  (a)  x + 4 = 5     ====>  x = 5-4 = 1.                                    ANSWER


    OR      (b)  -(x + 4) = 5  ====>  -x - 4 = 5  ====>  -5 - 4 = x  ====>  x = -9.    ANSWER


Answer.  The given equation has TWO SOLUTIONS  x= -9  and  x= 1

Solved.

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    - Absolute Value equations
in this site.

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