https://file.aiquickdraw.com/mathbot/file/1726372729791mt6kpmal.jpg

The equation in the image is:

\[
\frac{1}{7}(a + 6) = \frac{1}{3}(8 - a)
\]

Let's solve this step-by-step:

1. Distribute the fractions on both sides:

\[
\frac{1}{7} \times (a + 6) = \frac{1}{7}a + \frac{6}{7}
\]
\[
\frac{1}{3} \times (8 - a) = \frac{8}{3} - \frac{a}{3}
\]

This gives:

\[
\frac{1}{7}a + \frac{6}{7} = \frac{8}{3} - \frac{a}{3}
\]

2. Eliminate the fractions by multiplying through by the least common denominator (LCD), which is 21:

Multiply both sides by 21:

\[
21 \times \left(\frac{1}{7}a + \frac{6}{7}\right) = 21 \times \left(\frac{8}{3} - \frac{a}{3}\right)
\]

This simplifies to:

\[
3a + 18 = 56 - 7a
\]

3. Now, move all terms with \(a\) to one side and constant terms to the other:

\[
3a + 7a = 56 - 18
\]
\[
10a = 38
\]

4. Solve for \(a\):

\[
a = \frac{38}{10} = 3.8
\]

So, the solution to the equation is \(a = 3.8\).

Would you like further details on any step or have additional questions?

Here are some related questions you might find helpful:
1. How do you solve similar equations with fractions?
2. What happens when the equation includes negative signs inside the parentheses?
3. Can you explain how to handle equations with variables on both sides in more detail?
4. What if both sides of the equation had the same denominator—how would that simplify the problem?
5. How can I check if my solution to an equation is correct?

**Tip**: Always distribute and eliminate fractions as early as possible to simplify the equation and make solving it easier!

Solve the equation 1/7(a + 6) = 1/3(8 - a)

Learn how to solve the linear equation 1/7(a + 6) = 1/3(8 - a) step by step. This problem involves key algebraic concepts such as distributing fractions and simplifying equations with variables on both sides. Suitable for students in Grades 8-10.

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