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The equation to solve is:

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

Let's solve it step by step:

### Step 1: Eliminate the fractions
To eliminate the fractions, we need to find the least common denominator (LCD) of 5 and 3, which is 15. Multiply every term in the equation by 15:

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

This simplifies to:

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

### Step 2: Move the variable terms to one side
To get all the terms involving \(x\) on one side, subtract \(10x\) from both sides:

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

Simplifying:

\[
-16x + 45 = 5
\]

### Step 3: Move the constant terms to the other side
Now, subtract 45 from both sides:

\[
-16x = 5 - 45
\]

Simplifying:

\[
-16x = -40
\]

### Step 4: Solve for \(x\)
Finally, divide both sides by \(-16\):

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

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

Would you like any further clarification or details on any of the steps?

Here are 5 follow-up questions you could explore:
1. How do you solve equations with multiple fractions more efficiently?
2. Can this method be applied to equations with three or more terms?
3. What if the equation had an inequality instead of an equals sign?
4. How do you check the solution by substituting it back into the original equation?
5. What are the steps for solving systems of equations involving fractions?

**Tip:** Always check for the least common denominator when dealing with fractions in equations to simplify them early!

Solve the equation -2/5x + 3 = 2/3x + 1/3.

Learn how to solve the linear equation -2/5x + 3 = 2/3x + 1/3 step-by-step by eliminating fractions and simplifying. Ideal for students in Grades 8-10.

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