Let's solve the equation step by step:

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

### Step 1: Eliminate fractions
The common denominator of 5, 2, and 4 is 20. To eliminate the fractions, multiply both sides of the equation by 20:

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

This simplifies to:

\[
8x - 10x = -20x + 15
\]

### Step 2: Combine like terms
Now, combine like terms on both sides:

\[
8x - 10x = -2x
\]
So, the equation becomes:

\[
-2x = -20x + 15
\]

### Step 3: Move all terms involving \( x \) to one side
Add \( 20x \) to both sides of the equation:

\[
-2x + 20x = 15
\]

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 solve equations with variables on both sides?
2. What are common methods for dealing with fractions in algebraic equations?
3. How can you verify the solution to an equation?
4. How does multiplying both sides by the least common denominator help simplify equations?
5. How do you solve equations with more complex fractions?

**Tip:** Always double-check your work by substituting your solution back into the original equation.

Learn how to solve equations involving fractions step-by-step with an example problem. This problem covers algebraic concepts such as manipulating equations with fractions to find the solution. Suitable for Grades 9-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation