To solve for \( a \) in the equation \( a + c = \frac{b - a}{5} \), follow these steps:

### Step 1: Eliminate the fraction by multiplying both sides by 5.
\[
5(a + c) = b - a
\]

### Step 2: Distribute the 5 on the left side.
\[
5a + 5c = b - a
\]

### Step 3: Add \( a \) to both sides to combine like terms.
\[
6a + 5c = b
\]

### Step 4: Solve for \( a \).
\[
a = \frac{b - 5c}{6}
\]

So, the solution for \( a \) is:
\[
a = \frac{b - 5c}{6}
\]

Would you like any further details or have any questions? Here are some related questions you might find helpful:

1. How would the solution change if the fraction was different?
2. Can this equation be solved graphically? If so, how?
3. What happens if \( c \) equals zero? How does that affect \( a \)?
4. How do you solve similar equations with more variables?
5. How can you check if the solution is correct?

**Tip:** When dealing with fractions in equations, it's often helpful to eliminate the fraction early on by multiplying both sides by the denominator.

Learn how to solve the linear equation a + c = (b - a)/5 with a step-by-step approach. This problem covers essential algebraic techniques such as eliminating fractions and combining like terms. Suitable for students in Grades 8-10.

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