Qhat is the solution to |x+6|=2x-1

Question

The questin is what is the soluion to |x+6|=2x-1

Answer 1

Hi Brayan,
Remember absolute value problems have two possibilities that you have to solve separately:
Once you get an equation arranged so only the absolute value part is on one side: |inside| = magnitude, then rewrite it without the absolute value signs:
inside = +magnitude OR inside = –magnitude

For |x+6|=2x-1, separate the 2 possibilities:
x+6 = +(2x-1) OR x+6 = –(2x-1)

Then separately solve for x in each equation.
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<<Algebraic simplifications happen here.>>
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7 = x OR 3x = -5
So, possible solutions:
x = 7 OR x = -5/3

First. Note the two possible solutions for x are NOT ± of each other. The +6 as part of the inside makes the solutions not opposites.

Second. Note that if you substitute the second possible solution (-5/3) into the original equation, you get a negative answer on the right hand side and the left hand side, because of the absolute value signs, MUST be positive. So -5/3 is not a solution. 7 is the only solution.



Sue