https://file.aiquickdraw.com/mathbot/file/1727052690830znyhaj26.jpg

The equation provided in the image is:

\[
a = \frac{1}{2}(b + c - d)
\]

We are solving for \( b \). Let's go step by step:

### Step 1: Eliminate the fraction.
Multiply both sides of the equation by 2 to get rid of the \( \frac{1}{2} \):

\[
2a = b + c - d
\]

### Step 2: Solve for \( b \).
Now, isolate \( b \) by subtracting \( c - d \) from both sides:

\[
b = 2a - c + d
\]

Thus, the solution is:

\[
b = 2a - c + d
\]

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Would you like further details on any part of the solution? 

Here are some related questions:
1. How do you eliminate a fraction in an equation?
2. What are some other ways to rearrange this equation?
3. What happens if we solve for \( c \) instead of \( b \)?
4. How can this equation be used in a word problem context?
5. How does solving linear equations like this relate to algebraic manipulation?

**Tip:** When solving for a variable, always perform inverse operations (like adding or multiplying) to isolate the variable step-by-step.

Solve for b in the equation a = 1/2(b + c - d).

Discover how to solve for b in the linear equation a = 1/2(b + c - d). This problem involves basic algebraic manipulation, eliminating fractions, and isolating variables. Suitable for students in Grades 7-9.

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