SOLUTION: Whst is the absolute value of |x+6|=2x?

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Question 116169: Whst is the absolute value of |x+6|=2x?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The absolute value function has two values and you have to solve for both.
When (x+6)>0, then
abs%28x%2B6%29=x%2B6
x%2B6=2x
x=6
When (x+6)<0, then
abs%28x%2B6%29=-%28x%2B6%29
-%28x%2B6%29=2x
-x-6=2x
3x=-6
x=-2
Check your answers.
abs%28x%2B6%29=2x
abs%286%2B6%29=2%2A6
12=12
True statement.
Good answer.
abs%28x%2B6%29=2x
abs%28-2%2B6%29=2%2A%28-2%29
abs%284%29=-4
4=-4
False statement.
Not a good answer.
Here's why.
When we looked at the second solution,
we said "When (x+6)<0"
%28x%2B6%29%3C0
x%3C-6
We got an answer x=-2 which is not less than -6, so the answer is not valid.
There is only one solution.
x=6.