# Thread: Solving An Absolute Value Equation

1. ## Solving An Absolute Value Equation

How would I solve this equation for the inequality for x?

|2x + 2| = |x + 5|

2. ## Re: Solving An Absolute Value Equation

Originally Posted by Manni
How would I solve this equation for the inequality for x?

|2x + 2| = |x + 5|
What inequality? To solve this equation square both sides (since $x^2 \geq 0$ this will deal with the absolute value) but remember to check for extraneous solutions

3. ## Re: Solving An Absolute Value Equation

Would I use a similar approach when solving |x + 1| = 3|x + 2| + 5? And if so, how?

4. ## Re: Solving An Absolute Value Equation

Originally Posted by Manni
Would I use a similar approach when solving |x + 1| = 3|x + 2| + 5? And if so, how?
Yup. If $|f(x)| = |g(x)| + c$ then I'd use said method

5. ## Re: Solving An Absolute Value Equation

Gotcha! Thanks a lot

6. ## Re: Solving An Absolute Value Equation

Originally Posted by Manni
Gotcha! Thanks a lot
Did you get a solution ?

7. ## Re: Solving An Absolute Value Equation

Originally Posted by Manni
How would I solve this equation for the inequality for x?

|2x + 2| = |x + 5|
Either 2x + 2 & x + 5 have the same sign, in which case you have:
2x + 2 = x + 5
or they have opposite sign, in which case you have:
2x + 2 = -(x + 5).