https://file.aiquickdraw.com/mathbot/file/172598415205265j0cpev.jpg

The equation in the image is:

\[
\frac{3(x - 1)}{4} = \frac{3(x + 5)}{10}
\]

To solve for \( x \), let's first cross-multiply:

\[
3(x - 1) \cdot 10 = 3(x + 5) \cdot 4
\]

Simplify both sides:

\[
30(x - 1) = 12(x + 5)
\]

Now, expand both sides:

\[
30x - 30 = 12x + 60
\]

Next, we'll isolate \( x \) by moving all \( x \)-terms to one side and constants to the other:

\[
30x - 12x = 60 + 30
\]

Simplify:

\[
18x = 90
\]

Now, solve for \( x \):

\[
x = \frac{90}{18} = 5
\]

### Solution:
The value of \( x \) is **5**.

Would you like more details on this solution, or do you have any questions?

### Follow-up Questions:
1. How would you solve this equation if the fractions had different coefficients?
2. What happens if you have an equation with more variables?
3. Can you solve similar equations with a different method, such as substitution?
4. How would this change if the terms were squared?
5. How do you check if your solution is correct in this context?

**Tip:** Always cross-multiply when dealing with equations involving fractions to simplify the process.

Solve the equation 3(x - 1)/4 = 3(x + 5)/10 for x.

Learn how to solve the linear equation with fractions, 3(x - 1)/4 = 3(x + 5)/10, using cross-multiplication. This detailed step-by-step solution covers key algebraic concepts and is suitable for students in Grades 7-9.

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