Let's solve the equation \( a = b + d - a \) for \( a \).

### Step-by-step solution:

1. Start with the given equation:
   \[
   a = b + d - a
   \]

2. Add \( a \) to both sides to combine the \( a \)-terms:
   \[
   a + a = b + d
   \]

3. Simplify the left side:
   \[
   2a = b + d
   \]

4. Now, divide both sides by 2 to solve for \( a \):
   \[
   a = \frac{b + d}{2}
   \]

Thus, the solution is:
\[
a = \frac{b + d}{2}
\]

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. What happens if we subtract \( d \) from both sides in the original equation?
2. How would you solve if the equation was \( 2a = b + d - 3a \)?
3. Can you express \( b \) in terms of \( a \) and \( d \) from the equation \( a = b + d - a \)?
4. How would the solution change if \( d = 0 \)?
5. Can you graph the solution for specific values of \( b \) and \( d \)?

**Tip:** When solving equations, always combine like terms on each side before isolating the variable.

Learn how to solve the linear equation a = b + d - a for the variable a. This step-by-step solution explains basic algebraic concepts and simplifies the equation to a = (b + d) / 2. Suitable for students in Grades 6-8.

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