Question

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

Answer 1

To solve the absolute value equation \( 2|x - 3| - 4 = -4 \), we first start by isolating the absolute value term.

1. Add 4 to both sides:
\[
2|x - 3| - 4 + 4 = -4 + 4
\]
\[
2|x - 3| = 0
\]

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

3. The absolute value of an expression is zero only when the expression itself is zero. Therefore, we set the expression inside the absolute value to zero:
\[
x - 3 = 0
\]

4. Solving for \( x \), we find:
\[
x = 3
\]

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