Let's solve the equation step by step:

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

### Step 1: Eliminate fractions
To eliminate the fractions, find the least common denominator (LCD) for the fractions involved. The denominators are 5, 2, and 4. The LCD of 5, 2, and 4 is 20.

Multiply every term of the equation by 20 to eliminate the denominators:

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

This simplifies to:
\[
8x - 10x = -20x + 15
\]

### Step 2: Combine like terms
Now, simplify the equation by combining like terms:
\[
8x - 10x = -2x
\]
So the equation becomes:
\[
-2x = -20x + 15
\]

### Step 3: Move all terms involving \( x \) to one side
To eliminate \( x \) from the right-hand side, add \( 20x \) to both sides:
\[
-2x + 20x = 15
\]
Simplifying:
\[
18x = 15
\]

### Step 4: Solve for \( x \)
Now, divide both sides by 18:
\[
x = \frac{15}{18} = \frac{5}{6}
\]

### Final Answer:
The solution to the equation is:
\[
x = \frac{5}{6}
\]

Would you like further details, or do you have any questions?

Here are some related questions:
1. How do you handle negative signs when solving equations?
2. How can you check your solution to an equation?
3. What are the advantages of multiplying by the least common denominator?
4. How can solving linear equations help in real-world problems?
5. What methods can be used to simplify complex algebraic expressions?

**Tip:** When solving equations, keep track of your signs carefully to avoid errors.

Learn how to solve the equation 2x/5 - x/2 = -x + 3/4 with a detailed step-by-step solution. This problem involves equations with fractions and combining like terms. Suitable for students in Grades 7-9.

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