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

Question

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

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 \( x = 3 \).