Solve the absolute value equation.
StartAbsoluteValue 2 x minus 11 EndAbsoluteValue equals 17

We are given the equation:

\[
|2x - 11| = 17
\]

To solve this absolute value equation, we break it into two cases:

### Case 1: The expression inside the absolute value is positive or zero
\[
2x - 11 = 17
\]
Solving for \(x\):
\[
2x = 17 + 11
\]
\[
2x = 28
\]
\[
x = \frac{28}{2} = 14
\]

### Case 2: The expression inside the absolute value is negative
\[
2x - 11 = -17
\]
Solving for \(x\):
\[
2x = -17 + 11
\]
\[
2x = -6
\]
\[
x = \frac{-6}{2} = -3
\]

### Final Answer:
The solutions are:
\[
x = 14 \quad \text{or} \quad x = -3
\]

Would you like more details on any step or have any further questions?

Here are 5 related questions to explore:
1. How do you graph absolute value functions?
2. What is the geometric meaning of absolute value equations?
3. How do you solve inequalities involving absolute values?
4. What are the properties of absolute value that help in solving such equations?
5. How would the solution change if the equation was \( |2x - 11| = -17 \)?

**Tip**: When solving absolute value equations, always remember to check both the positive and negative cases!

Solve the absolute value equation. |2x - 11| = 17

Learn how to solve the absolute value equation |2x - 11| = 17 with a detailed step-by-step breakdown. This problem covers key algebraic concepts, including handling absolute value equations and applying the Absolute Value Theorem. Suitable for students in Grades 7-9.

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