https://file.aiquickdraw.com/mathbot/file/17298259607264a5gcy52.jpg

The equation shown in the image is:

\[
\frac{1}{6}(b + c - d) = a
\]

We are asked to solve for \( b \). Let's go through the steps:

1. **Multiply both sides by 6** to eliminate the fraction:
   \[
   b + c - d = 6a
   \]

2. **Isolate \( b \)** by subtracting \( c \) and adding \( d \) to both sides:
   \[
   b = 6a - c + d
   \]

Thus, the solution for \( b \) is:
\[
b = 6a - c + d
\]

Would you like any more details or have any questions?

Here are 5 related questions to practice further:
1. How would the equation change if instead of \( \frac{1}{6} \), you had \( \frac{1}{3} \)?
2. What happens if \( c = d \) in the equation?
3. Can you solve for \( d \) instead of \( b \) in this case?
4. If \( a = 2 \), \( c = 4 \), and \( d = 1 \), what is the value of \( b \)?
5. What is the effect of multiplying both sides of the equation by a constant on the variables?

**Tip:** Always eliminate fractions by multiplying through by the denominator for simpler algebraic manipulations!

Learn how to solve the linear equation (1/6)(b + c - d) = a for the variable b. This algebraic problem involves multiplying through by the denominator to eliminate the fraction, followed by isolating the variable. Suitable for students in Grades 7-9.

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