To solve the equation \( 3x + \frac{5}{3} + \frac{7}{3} = \frac{-3x}{5} \), follow these steps:

1. **Combine like terms on the left side**:
   \[
   3x + \frac{5}{3} + \frac{7}{3} = 3x + \frac{12}{3} = 3x + 4
   \]
   So the equation becomes:
   \[
   3x + 4 = \frac{-3x}{5}
   \]

2. **Eliminate the fraction by multiplying the entire equation by 5** (to get rid of the denominator on the right side):
   \[
   5(3x + 4) = 5\left(\frac{-3x}{5}\right)
   \]
   This simplifies to:
   \[
   15x + 20 = -3x
   \]

3. **Move all terms involving \(x\) to one side** and constants to the other side:
   \[
   15x + 3x = -20
   \]
   \[
   18x = -20
   \]

4. **Solve for \(x\)** by dividing both sides by 18:
   \[
   x = \frac{-20}{18} = \frac{-10}{9}
   \]

So, the solution is:
\[
x = \frac{-10}{9}
\]

Would you like further details on any of these steps?

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Here are 5 related questions for further practice:

1. Solve the equation \(2x + \frac{4}{5} + \frac{6}{5} = \frac{-2x}{4}\).
2. If \(5x + \frac{8}{4} + \frac{2}{4} = \frac{-5x}{3}\), what is the value of \(x\)?
3. Solve for \(x\): \(4x + \frac{10}{2} - \frac{3}{2} = \frac{-4x}{6}\).
4. What is the solution to \(7x + \frac{9}{3} + \frac{1}{3} = \frac{-7x}{2}\)?
5. Determine the value of \(x\) in the equation \(x + \frac{15}{5} - \frac{7}{5} = \frac{-x}{7}\).

**Tip:** Always look for opportunities to simplify an equation by combining like terms or eliminating fractions early on.

Learn how to solve the linear equation 3x + 5/3 + 7/3 = -3x/5 with a detailed step-by-step solution. This problem involves key algebraic concepts such as combining like terms and solving equations with fractions. Suitable for students in Grades 7-9.

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