\frac{-\left(3a-4\right)+6}{-5} what does a equal

To find what \( a \) equals in the expression

\[
\frac{-\left(3a-4\right)+6}{-5}
\]

we need to simplify the expression and solve for \( a \).

### Step 1: Simplify the numerator
The numerator is \( -\left(3a - 4\right) + 6 \).

Distribute the negative sign across \( (3a - 4) \):

\[
- \left(3a - 4\right) = -3a + 4
\]

Now add 6 to this:

\[
-3a + 4 + 6 = -3a + 10
\]

### Step 2: Rewrite the expression
Now the original expression becomes:

\[
\frac{-3a + 10}{-5}
\]

### Step 3: Simplify the fraction
Since both the numerator and the denominator have negatives, we can cancel out the negative signs:

\[
\frac{-3a + 10}{-5} = \frac{3a - 10}{5}
\]

This is the simplified expression. There is no equality set up here, so there is no specific solution for \( a \). If you need to solve for \( a \), more information would be required, such as setting this expression equal to a particular value.

Would you like more details or clarification?

Here are 5 related questions to explore further:
1. What happens when you set \( \frac{3a - 10}{5} = 0 \)?
2. How would the expression change if the numerator had different constants?
3. How do you solve for \( a \) if \( \frac{3a - 10}{5} = 2 \)?
4. Can you rearrange the expression into a different form before simplifying?
5. How does factoring affect the simplification of similar expressions?

**Tip:** Always distribute negative signs carefully, as they change the signs of every term inside parentheses.

Explore how to simplify the algebraic expression \frac{-\left(3a-4\right)+6}{-5}. This step-by-step guide covers the distributive property and simplifying fractions, making it suitable for students in Grades 8-10.

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