To check if \( \frac{2}{3} a = -8 \) is true, we can substitute the value of \( a \) and see if it satisfies the equation.

### Solution:

1. Start with the equation:
   \[
   \frac{2}{3} a = -8
   \]

2. To isolate \( a \), multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):
   \[
   a = -8 \times \frac{3}{2}
   \]

3. Calculate the right side:
   \[
   a = -12
   \]

### Verification
Now that we have \( a = -12 \), substitute this value back into the original equation to check if it holds.

1. Substitute \( a = -12 \) into \( \frac{2}{3} a = -8 \):
   \[
   \frac{2}{3} \times -12 = -8
   \]

2. Calculate the left side:
   \[
   -8 = -8
   \]

Since both sides are equal, the equation is correct when \( a = -12 \).

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Would you like a further breakdown or have any questions about this solution?

### Related Questions

1. What if \( \frac{2}{3} a = 10 \)? What would \( a \) be?
2. How do we solve \( \frac{3}{4} x = -6 \)?
3. What happens if we change the fraction to \( \frac{4}{5} a = -8 \)?
4. How can you solve an equation like \( 2a + \frac{3}{2} = -10 \)?
5. Why do we use the reciprocal when isolating variables in fractional equations?

#### Tip:
To solve equations with fractions, multiplying by the reciprocal is often the quickest way to isolate the variable.

Discover how to solve the equation 2/3 a = -8 with a clear step-by-step explanation. This guide covers isolating variables, checking solutions, and key algebraic concepts suitable for students in Grades 6-8.

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