Let's solve the equation step by step:

\[
c + \frac{8}{5} - 6 = 4 - c
\]

1. First, isolate terms with \(c\) on one side. We can move \(c\) from the right-hand side to the left-hand side by adding \(c\) to both sides of the equation:

\[
c + \frac{8}{5} - 6 + c = 4
\]

This simplifies to:

\[
2c + \frac{8}{5} - 6 = 4
\]

2. Next, simplify the constants. We have \(-6\) and \(\frac{8}{5}\). To combine these, we convert \(-6\) into a fraction with denominator 5:

\[
-6 = \frac{-30}{5}
\]

So the equation becomes:

\[
2c + \frac{8}{5} - \frac{30}{5} = 4
\]

3. Combine the fractions on the left-hand side:

\[
2c + \frac{8 - 30}{5} = 4
\]

\[
2c + \frac{-22}{5} = 4
\]

4. Now, move \(\frac{-22}{5}\) to the other side by adding \(\frac{22}{5}\) to both sides:

\[
2c = 4 + \frac{22}{5}
\]

5. To add \(4\) and \(\frac{22}{5}\), convert 4 into a fraction with denominator 5:

\[
4 = \frac{20}{5}
\]

Now add the fractions:

\[
2c = \frac{20}{5} + \frac{22}{5} = \frac{42}{5}
\]

6. Finally, divide both sides of the equation by 2 to isolate \(c\):

\[
c = \frac{\frac{42}{5}}{2} = \frac{42}{5} \times \frac{1}{2} = \frac{42}{10} = \frac{21}{5}
\]

So the solution is:

\[
c = \frac{21}{5}
\]

Would you like further clarification on any of the steps or have any other questions? Here are some related questions you can explore:

1. How do you solve equations involving fractions?
2. What methods can you use to combine terms with different denominators?
3. How do you handle variables on both sides of an equation?
4. What is the significance of isolating the variable in an equation?
5. How do you convert between mixed numbers and improper fractions?

**Tip:** When solving equations with fractions, it's often helpful to first get rid of fractions by multiplying both sides of the equation by the least common denominator (LCD).

Learn how to solve the linear equation c + 8/5 - 6 = 4 - c, including how to handle fractions and combine terms on both sides of the equation. This detailed guide is suitable for students in Grades 7-9, covering key algebraic techniques such as isolating variables and fraction manipulation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation