The given equation is:

\[
\frac{4}{3} = \frac{3}{2}c + \frac{5}{3}
\]

To solve for \( c \), let's go step by step.

### Step 1: Eliminate the fractions
Multiply through by the least common denominator (LCD) of the fractions, which is 6, to clear the fractions.

\[
6 \times \left( \frac{4}{3} \right) = 6 \times \left( \frac{3}{2}c \right) + 6 \times \left( \frac{5}{3} \right)
\]

This simplifies to:

\[
8 = 9c + 10
\]

### Step 2: Solve for \( c \)
Now, subtract 10 from both sides:

\[
8 - 10 = 9c
\]

\[
-2 = 9c
\]

### Step 3: Isolate \( c \)
Finally, divide both sides by 9:

\[
c = \frac{-2}{9}
\]

Thus, the value of \( c \) is \( \frac{-2}{9} \).

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How would you solve if the equation had a different constant on the right side?
2. Can you solve \( \frac{5}{4} = \frac{7}{3}c + \frac{2}{5} \)?
3. How do you handle equations with variables in the denominator?
4. What happens if the fractions don't have a common denominator?
5. How can this method be applied to a system of equations?

**Tip**: Clearing fractions by multiplying with the least common denominator simplifies solving equations with multiple fractions.

Learn how to solve the linear equation 4/3 = 3/2c + 5/3 with a step-by-step guide. This problem focuses on algebraic concepts involving fractions and is suitable for students in Grades 7-9.

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