We are given the equation:

$5 - 2|x - 3| = 3$

Step-by-Step Solution:

1. Isolate the absolute value expression:

$5 - 2|x - 3| = 3$

Subtract 5 from both sides:

$-2|x - 3| = 3 - 5$

$-2|x - 3| = -2$

2. Divide both sides by -2 to simplify:

$|x - 3| = 1$

3. Solve the absolute value equation:

The absolute value equation $|x - 3| = 1$ gives two possible equations:

$x - 3 = 1 \quad \text{or} \quad x - 3 = -1$

4. Solve each equation:

• For $x - 3 = 1$:

$x = 1 + 3 = 4$

• For $x - 3 = -1$:

$x = -1 + 3 = 2$

Final Answer:

The solutions are:

$x = 2 \quad \text{or} \quad x = 4$

Do you need further clarification on any steps or want more details?

Here are 5 related questions:

1. What if the equation was $5 - 2|x - 3| = 6$?
2. How do you handle absolute value inequalities like $|x - 3| \leq 2$?
3. What happens when you divide an absolute value equation by a negative number?
4. How can you check if your solutions for absolute value equations are correct?
5. Can you have an absolute value equation with no solutions?

Tip: When solving absolute value equations, always check for two cases: one where the expression inside the absolute value is positive and one where it is negative.