To solve the absolute value equation \( |26 - 4c| = 10 \), we need to consider the definition of absolute value, which states that for \( |x| = a \), either \( x = a \) or \( x = -a \).

### Step-by-step solution:

1. \( 26 - 4c = 10 \)
2. \( 26 - 4c = -10 \)

Now, solve each equation:

#### For \( 26 - 4c = 10 \):
\[
26 - 4c = 10
\]
\[
-4c = 10 - 26
\]
\[
-4c = -16
\]
\[
c = \frac{-16}{-4} = 4
\]

#### For \( 26 - 4c = -10 \):
\[
26 - 4c = -10
\]
\[
-4c = -10 - 26
\]
\[
-4c = -36
\]
\[
c = \frac{-36}{-4} = 9
\]

### Solution:
The solutions are \( c = 4 \) and \( c = 9 \).

Would you like more details on absolute value equations?

Here are 5 related questions to explore further:
1. How do you solve an absolute value inequality like \( |x - 3| \geq 7 \)?
2. What happens if the absolute value equation has no solution?
3. Can an absolute value equation have a fractional solution?
4. How would you graph the solutions to \( |x - a| = b \)?
5. What is the geometric interpretation of absolute value?

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

Learn how to solve the absolute value equation |26 - 4c| = 10 using the step-by-step method. This solution covers key algebraic concepts such as absolute value properties and provides both solutions: c = 4 and c = 9. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation