Let's solve the equation:

\[
-\frac{2}{5}x + 3 = \frac{2}{3}x + \frac{1}{3}
\]

### Step 1: Eliminate the fractions
To clear the fractions, find the least common denominator (LCD) of 5 and 3, which is 15. Multiply both sides of the equation by 15:

\[
15\left(-\frac{2}{5}x + 3\right) = 15\left(\frac{2}{3}x + \frac{1}{3}\right)
\]

Distribute 15 on both sides:

\[
15 \times -\frac{2}{5}x + 15 \times 3 = 15 \times \frac{2}{3}x + 15 \times \frac{1}{3}
\]

This simplifies to:

\[
-6x + 45 = 10x + 5
\]

### Step 2: Move the variables to one side
Now, subtract \(10x\) from both sides:

\[
-6x - 10x + 45 = 5
\]

Simplifying:

\[
-16x + 45 = 5
\]

### Step 3: Isolate \(x\)
Subtract 45 from both sides:

\[
-16x = 5 - 45
\]

Simplifying:

\[
-16x = -40
\]

### Step 4: Solve for \(x\)
Divide both sides by -16:

\[
x = \frac{-40}{-16}
\]

Simplify the fraction:

\[
x = \frac{40}{16} = \frac{5}{2}
\]

### Final Answer:
\[
x = \frac{5}{2}
\]

Would you like any further clarification or details on this?

Here are some related questions to consider:
1. What happens when the equation involves more complex fractions?
2. How do you solve equations with variables on both sides?
3. Can we solve equations using decimals instead of fractions?
4. What are other methods to eliminate fractions in equations?
5. How does changing the coefficients affect the solution?

**Tip:** Always check for common denominators when working with fractions to simplify solving!

This page provides a detailed step-by-step solution for solving the linear equation -2/5x + 3 = 2/3x + 1/3. Learn how to handle equations with fractions by clearing the denominators and isolating the variable. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation