https://file.aiquickdraw.com/mathbot/file/1727381002278nw7uoa16.jpg

The equation in the image is:

\[
\frac{2x - 5}{3} + 2 = \frac{3}{4}
\]

Let's solve it step by step.

### Step 1: Subtract 2 from both sides
To eliminate the constant term on the left-hand side, subtract 2 from both sides:

\[
\frac{2x - 5}{3} = \frac{3}{4} - 2
\]

First, convert \(2\) to a fraction with a denominator of 4:

\[
2 = \frac{8}{4}
\]

Now subtract:

\[
\frac{3}{4} - \frac{8}{4} = \frac{-5}{4}
\]

So the equation becomes:

\[
\frac{2x - 5}{3} = \frac{-5}{4}
\]

### Step 2: Cross multiply
Now, to eliminate the fractions, cross multiply:

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

This simplifies to:

\[
8x - 20 = -15
\]

### Step 3: Solve for \(x\)
Add 20 to both sides:

\[
8x = -15 + 20
\]

\[
8x = 5
\]

Finally, divide both sides by 8:

\[
x = \frac{5}{8}
\]

### Final Answer:
\[
x = \frac{5}{8}
\]

Let me know if you need further details or clarification!

Here are some related questions for further practice:
1. How do you handle equations with more complex fractions?
2. What happens when there are variables in the denominator as well?
3. How can we solve quadratic equations with fractions?
4. What is the effect of adding or subtracting fractions with different denominators?
5. How do you check if your solution to an equation is correct?

**Tip:** When solving equations with fractions, it's often useful to find a common denominator early to simplify the process.

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

This solution demonstrates how to solve the linear equation (2x - 5) / 3 + 2 = 3 / 4. Learn how to work with fractions, perform cross multiplication, and simplify the expression step-by-step. Suitable for students in Grades 7-9.

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