To solve the equation \( a = 2(b - c) \) for \( b \), follow these steps:

1. **Distribute the 2 on the right side:**

\[
a = 2b - 2c
\]

2. **Isolate the term containing \( b \) by adding \( 2c \) to both sides:**

\[
a + 2c = 2b
\]

3. **Solve for \( b \) by dividing both sides by 2:**

\[
b = \frac{a + 2c}{2}
\]

Thus, the solution for \( b \) is:

\[
\boxed{b = \frac{a + 2c}{2}}
\]

Would you like a more detailed explanation or have any questions?

### Related Questions:

1. How would you solve for \( c \) in the equation \( a = 2(b - c) \)?
2. If \( a = 10 \) and \( c = 3 \), what is the value of \( b \)?
3. What happens to the value of \( b \) if \( a \) is doubled?
4. How can this equation be represented graphically?
5. What if the equation was \( a = 3(b - c) \) instead?

**Tip:** Remember that isolating a variable involves performing inverse operations to both sides of the equation.

This page provides a step-by-step solution to the linear equation a = 2(b - c) for the variable b. Learn key algebraic concepts and formulas to solve for b, suitable for students in Grades 8-10.

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