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 start by isolating the absolute value expression.

1. Add 4 to both sides of the equation:
\[
2|x - 3| - 4 + 4 = -4 + 4
\]
This simplifies to:
\[
2|x - 3| = 0
\]

2. Now divide both sides by 2:
\[
|x - 3| = 0
\]

3. The absolute value equals zero when the expression inside it equals zero:
\[
x - 3 = 0
\]

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

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