Solve each absolute value equation.

3 + |x| = 5

My work:

3 + x = 5 or 3 + x = -5

x = 2 or x = -8

The book says that I am wrong. I do not know why.

Close, but you have to subtract 3 from both sides first.

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

OHHH! I see. Thanks alot!

To solve the absolute value equation 3 + |x| = 5, you need to consider both possible scenarios for the absolute value term: |x| could equal x or -x, depending on whether x is positive or negative.

Let's break down the equation using these two possibilities:

Case 1: x is positive or zero (x ≥ 0)
In this case, |x| = x. So we rewrite the equation as:
3 + x = 5

Now, isolate x by subtracting 3 from both sides:
x = 5 - 3
x = 2

Therefore, we have one solution: x = 2.

Case 2: x is negative (x < 0)
In this case, |x| = -x. So we rewrite the equation as:
3 - x = 5

Now, isolate x by subtracting 3 from both sides:
-x = 5 - 3
-x = 2

To solve for x, multiply both sides by -1 (or divide by -1 since we have a negative sign):
x = -2

Therefore, we have another solution: x = -2.

So, the solutions to the original equation 3 + |x| = 5 are x = 2 and x = -2.

If the book says you are wrong, it's possible that there might be an error either in your work or in the book's answer key. Double-check your calculations and the steps you followed to solve the equation.