To solve the equation \( \frac{4x}{5} + \frac{2x}{5} = -\frac{12}{5} \), we can follow these steps:

1. Combine the like terms on the left-hand side:
   \[
   \frac{4x}{5} + \frac{2x}{5} = \frac{6x}{5}
   \]
   So, the equation becomes:
   \[
   \frac{6x}{5} = -\frac{12}{5}
   \]

2. To eliminate the fraction, multiply both sides of the equation by 5:
   \[
   6x = -12
   \]

3. Solve for \( x \) by dividing both sides by 6:
   \[
   x = \frac{-12}{6}
   \]
   \[
   x = -2
   \]

So, the solution to the equation is \( x = -2 \).

Would you like any more details or have any questions?

Here are 8 related questions to expand your understanding:

1. How do you solve \(\frac{3x}{4} + \frac{5x}{4} = 2\)?
2. What is the solution to \( \frac{7x}{3} - \frac{2x}{3} = 1\)?
3. How would you solve \( \frac{5x}{6} + \frac{x}{3} = -\frac{7}{2} \)?
4. What steps are needed to solve \( 4x + 2 = 10 \)?
5. How do you handle equations with fractions, like \( \frac{3x+1}{4} = 2 \)?
6. Can you solve \( \frac{x}{2} + \frac{3}{2} = 5 \)?
7. What is the process for solving \( 6x - 4 = 2x + 8 \)?
8. How do you solve \( \frac{2x}{5} + \frac{3x}{10} = 1 \)?

**Tip:** When dealing with fractions in equations, it's often helpful to multiply through by the denominator to clear the fractions and simplify the solving process.

Learn how to solve the equation 4x/5 + 2x/5 = -12/5 step-by-step with detailed explanation and calculations. This problem involves solving linear equations with fractions. Suitable for students in Grades 7-9.

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