Solve for cc.
82, equals, 6, plus, start fraction, 4, divided by, 5, end fraction, c
82=
6+ 
5
4
​
 c

We are given the equation:

\[
82 = 6 + \frac{4}{5}c
\]

To solve for \( c \), follow these steps:

### Step 1: Subtract 6 from both sides of the equation

\[
82 - 6 = \frac{4}{5}c
\]

\[
76 = \frac{4}{5}c
\]

### Step 2: Multiply both sides by \( \frac{5}{4} \) to isolate \( c \)

\[
c = 76 \times \frac{5}{4}
\]

\[
c = \frac{76 \times 5}{4}
\]

\[
c = \frac{380}{4}
\]

### Step 3: Simplify the fraction

\[
c = 95
\]

Thus, \( c = 95 \).

---

Would you like a more detailed breakdown of any step or clarification on anything? Here are some follow-up questions:

1. How do we solve equations with fractions on one side?
2. How can we solve equations with decimals and fractions together?
3. What would happen if the constant term (6) were a fraction instead of an integer?
4. How do we handle solving for variables when they appear in both the numerator and denominator?
5. What if the equation was a quadratic one instead of linear?

Tip: When working with fractions, multiplying both sides by the denominator is often a quick way to eliminate the fraction.

Learn how to solve the linear equation 82 = 6 + 4/5c with a detailed, step-by-step breakdown. This problem involves solving for a variable in an equation with fractions. Suitable for students in Grades 6-8.

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