https://file.aiquickdraw.com/mathbot/file/1727191683053cy1wbs5n.jpg

The equation in the image is:

\[
\frac{\frac{2}{3}(x - 1)}{2} = \frac{\frac{2}{3}(x - 3)}{8}
\]

We need to find the value of \( x \). Let's solve this step-by-step.

1. Multiply both sides of the equation by 8 to eliminate the denominator on the right side:
\[
8 \times \frac{\frac{2}{3}(x - 1)}{2} = \frac{2}{3}(x - 3)
\]

This simplifies to:
\[
4 \times \frac{2}{3}(x - 1) = \frac{2}{3}(x - 3)
\]

2. Now, multiply through by 4 on the left side:
\[
\frac{8}{3}(x - 1) = \frac{2}{3}(x - 3)
\]

3. Eliminate the fractions by multiplying through the entire equation by 3:
\[
8(x - 1) = 2(x - 3)
\]

4. Expand both sides:
\[
8x - 8 = 2x - 6
\]

5. Bring all terms involving \( x \) to one side and constant terms to the other:
\[
8x - 2x = -6 + 8
\]

Simplifying this gives:
\[
6x = 2
\]

6. Solve for \( x \):
\[
x = \frac{2}{6} = \frac{1}{3}
\]

Thus, the value of \( x \) is \( \frac{1}{3} \).

Would you like further explanation or details on this solution?

Here are some related questions for practice:
1. Solve \( \frac{\frac{4}{5}(x - 2)}{3} = \frac{\frac{6}{7}(x + 1)}{5} \).
2. Solve \( \frac{2}{x+1} = \frac{4}{x-1} \) for \( x \).
3. If \( \frac{a}{b} = \frac{c}{d} \), express \( a \) in terms of \( b, c, \) and \( d \).
4. Solve \( \frac{3x - 5}{4} = \frac{x + 7}{2} \).
5. If \( \frac{2}{x-1} = \frac{5}{x+1} \), find \( x \).

**Tip**: Always try to eliminate fractions early in the equation to simplify the problem.

Find the value of x in the equation: (2/3(x - 1)) / 2 = (2/3(x - 3)) / 8

Learn how to solve the rational equation (2/3(x - 1)) / 2 = (2/3(x - 3)) / 8. This step-by-step solution demonstrates algebraic manipulation techniques like cross multiplication. Suitable for students in Grades 8-10.

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