solve this 2x/3 + 8x/9 to find value of x

To solve the equation \( \frac{2x}{3} + \frac{8x}{9} = 0 \), follow these steps:

1. **Find a common denominator** for the fractions:

   The denominators are 3 and 9. The least common denominator (LCD) is 9.

2. **Rewrite each fraction** with the common denominator:

   \[
   \frac{2x}{3} = \frac{2x \times 3}{3 \times 3} = \frac{6x}{9}
   \]
   
   So, the equation becomes:
   
   \[
   \frac{6x}{9} + \frac{8x}{9} = 0
   \]

3. **Combine the fractions**:

   \[
   \frac{6x + 8x}{9} = \frac{14x}{9}
   \]

   The equation is now:

   \[
   \frac{14x}{9} = 0
   \]

4. **Solve for \( x \)**:

   Since a fraction is zero only when its numerator is zero, set the numerator equal to zero:
   
   \[
   14x = 0
   \]
   
   Divide both sides by 14:
   
   \[
   x = 0
   \]

So, the value of \( x \) is \( 0 \).

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. Solve \( \frac{3x}{5} + \frac{7x}{10} = 0 \).
2. If \( \frac{4x}{7} + \frac{5x}{14} = 0 \), what is \( x \)?
3. Solve \( \frac{x}{2} - \frac{x}{3} = 0 \).
4. Find the value of \( x \) in \( \frac{5x}{8} + \frac{3x}{4} = 0 \).
5. What is the value of \( x \) when \( \frac{6x}{11} - \frac{2x}{11} = 0 \)?

**Tip:** When combining fractions, always find the least common denominator to simplify your work.

Learn how to solve the fractional equation 2x/3 + 8x/9 to find the value of x with a detailed step-by-step solution. This problem covers key concepts in fractions and equations. Suitable for students in Grades 7-9.

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