https://file.aiquickdraw.com/mathbot/file/1729260294891te1ybcqx.jpg

The equation shown in the image is:

\[
\frac{3(x - 2)}{4} - \frac{2(x + 1)}{5} = \frac{1}{10}
\]

Let's solve this step by step.

### Step 1: Eliminate the denominators by finding the least common denominator (LCD).
The denominators are 4, 5, and 10. The LCD of 4, 5, and 10 is 20. We multiply every term in the equation by 20 to eliminate the fractions.

\[
20 \cdot \left(\frac{3(x - 2)}{4}\right) - 20 \cdot \left(\frac{2(x + 1)}{5}\right) = 20 \cdot \left(\frac{1}{10}\right)
\]

Simplifying each term:

\[
5 \cdot 3(x - 2) - 4 \cdot 2(x + 1) = 2
\]

### Step 2: Distribute the constants.
Now distribute the 5 and 4 inside the parentheses:

\[
15(x - 2) - 8(x + 1) = 2
\]

\[
15x - 30 - 8x - 8 = 2
\]

### Step 3: Combine like terms.
Combine the \(x\)-terms and constant terms:

\[
(15x - 8x) = 7x
\]
\[
(-30 - 8) = -38
\]

So the equation becomes:

\[
7x - 38 = 2
\]

### Step 4: Solve for \(x\).
Add 38 to both sides:

\[
7x = 2 + 38
\]
\[
7x = 40
\]

Now divide by 7:

\[
x = \frac{40}{7}
\]

Thus, the solution is:

\[
x = \frac{40}{7}
\]

Would you like further explanation on any step, or help with another problem?

Here are 5 related questions to consider:
1. What are other methods to solve linear equations with fractions?
2. Can this equation be solved by graphing, and how would the solution look graphically?
3. What are the steps to check if the solution \(x = \frac{40}{7}\) is correct?
4. How would this equation change if the constant term on the right-hand side was a variable instead?
5. What are some real-world applications of solving linear equations like this one?

**Tip:** When solving equations with fractions, clearing the denominators early on can simplify the process and reduce potential mistakes.

Solve the equation: 3(x - 2)/4 - 2(x + 1)/5 = 1/10

This guide walks you through solving the linear equation 3(x - 2)/4 - 2(x + 1)/5 = 1/10 step by step. Learn how to eliminate denominators, distribute constants, and combine like terms to find the solution x = 40/7. Suitable for high school students in Grades 9-12.

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