Solve for all values of xx in simplest form.
5, minus, 2, vertical bar, x, minus, 3, vertical bar, equals, 3
5−2∣x−3∣=
3

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.

Solve for all values of x in simplest form: 5 − 2|x − 3| = 3

Learn how to solve the absolute value equation 5 − 2|x − 3| = 3 with a clear step-by-step explanation. This solution covers algebraic concepts like isolating absolute values, handling linear equations, and solving absolute value equations. Ideal for students in Grades 7-9.

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