Question

Solve the absolute value equation 2|x−3|−4=−4
.(1 point)
The solution to the absolute value equation is x=
.

Answer 1

To solve the equation \( 2|x−3|−4=−4 \), we first simplify it step by step.

1. Start by isolating the absolute value term:
\[
2|x−3| - 4 = -4
\]
Add 4 to both sides:
\[
2|x−3| = 0
\]

2. Divide both sides by 2:
\[
|x−3| = 0
\]

3. The absolute value of a number is zero when the number itself is zero:
\[
x - 3 = 0
\]

4. Solve for \(x\):
\[
x = 3
\]

Therefore, the solution to the absolute value equation is \( x = 3 \).