https://file.aiquickdraw.com/mathbot/file/1728310678040qnwxaloc.jpg

The equation given in the image is:

\[
45 = |c - 20|
\]

To solve for \( c \), we need to consider the two possible cases for the absolute value expression:

### Case 1: \( c - 20 = 45 \)
\[
c = 45 + 20 = 65
\]

### Case 2: \( c - 20 = -45 \)
\[
c = -45 + 20 = -25
\]

Thus, the two solutions for \( c \) are:

\[
c = 65 \quad \text{or} \quad c = -25
\]

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do we solve absolute value equations in general?
2. What happens when the number on the right side of the absolute value equation is negative?
3. Can you graph the solution for \( |c - 20| = 45 \)?
4. How would you verify the solutions to this equation?
5. What if the equation were \( |c + 20| = 45 \)? How would the solutions change?

**Tip:** Always check both possible cases in absolute value equations to find all solutions.

Solve for all values of c in simplest form: 45 = |c - 20|

Learn how to solve the absolute value equation 45 = |c - 20| with detailed steps and multiple solutions. Explore how absolute value properties lead to two possible answers, suitable for Grades 8-10.

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