Solve for all values of cc in simplest form.
open vertical bar, minus, 4, c, plus, 13, close vertical bar, equals, 15
∣−4c+13∣=
15

To solve the equation \( | -4c + 13 | = 15 \), we need to consider the two cases of absolute value.

### Case 1: Positive case
\[
-4c + 13 = 15
\]
Solve for \( c \):
\[
-4c = 15 - 13
\]
\[
-4c = 2
\]
\[
c = \frac{2}{-4} = -\frac{1}{2}
\]

### Case 2: Negative case
\[
-4c + 13 = -15
\]
Solve for \( c \):
\[
-4c = -15 - 13
\]
\[
-4c = -28
\]
\[
c = \frac{-28}{-4} = 7
\]

### Final Answer:
The solutions for \( c \) are:
\[
c = -\frac{1}{2} \quad \text{or} \quad c = 7
\]

Would you like any further details on this process?

Here are 5 related questions:
1. What are the properties of absolute value functions?
2. How can we graph the function \( y = | -4c + 13 | \)?
3. How do we handle absolute value inequalities?
4. What happens if the right-hand side of the absolute value equation is negative?
5. How do you solve absolute value equations with variables on both sides?

**Tip**: Always remember to check for extraneous solutions when solving absolute value equations, especially when additional constraints are involved.

Solve for all values of c in simplest form: |−4c + 13| = 15

Learn how to solve the absolute value equation |−4c + 13| = 15 with a detailed step-by-step solution. This problem covers key algebraic concepts, including absolute value properties and solving linear equations. Suitable for students in Grades 8-10.

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