Solve the absolute value equation 2|x−3|−4=−4

Question

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

Answer 1

To solve the equation \( 2|x - 3| - 4 = -4 \), we can 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. Divide both sides by 2: \[ |x - 3| = 0 \]

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

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

The solution to the absolute value equation is: \[ \boxed{3} \]