Question

Calculat the absolute value of: 4-{x-3}=0

Answer 1

To solve the equation \( 4 - |x - 3| = 0 \), first, let's isolate the absolute value term:

\[
4 = |x - 3|
\]

Now, we can break it down into two cases based on the definition of absolute value.

1. **Case 1**: \( x - 3 = 4 \)

\[
x - 3 = 4 \\
x = 4 + 3 \\
x = 7
\]

2. **Case 2**: \( x - 3 = -4 \)

\[
x - 3 = -4 \\
x = -4 + 3 \\
x = -1
\]

Thus, the solutions to the equation \( 4 - |x - 3| = 0 \) are:

\[
x = 7 \quad \text{and} \quad x = -1
\]

Both \( x = 7 \) and \( x = -1 \) are valid solutions.