To solve the equation \( 45 = |c - 20| \), we need to consider the definition of the absolute value. The absolute value equation \( |x| = a \) can be solved as:

\[
x = a \quad \text{or} \quad x = -a
\]

So for \( 45 = |c - 20| \), we have:

\[
c - 20 = 45 \quad \text{or} \quad c - 20 = -45
\]

Now, solve each equation separately:

1. \( c - 20 = 45 \)
   \[
   c = 45 + 20
   \]
   \[
   c = 65
   \]

2. \( c - 20 = -45 \)
   \[
   c = -45 + 20
   \]
   \[
   c = -25
   \]

So the solutions are \( c = 65 \) or \( c = -25 \).

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you solve equations with multiple absolute value expressions?
2. What happens when you add or subtract a constant inside an absolute value?
3. Can absolute value equations have no solutions?
4. How can absolute value inequalities be solved?
5. What are the applications of absolute value equations in real-world problems?

**Tip:** When solving absolute value equations, always consider both the positive and negative scenarios.

Learn how to solve the absolute value equation |c - 20| = 45 with a detailed step-by-step solution. This problem covers key concepts in algebra, including absolute value equations and their solutions. Suitable for students in Grades 9-12.

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