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Let's solve the given equation:

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

### Step 1: Eliminate the fractions
We can clear the fractions by multiplying the entire equation by the least common denominator (LCD) of all the fractions. The LCD of 5 and 3 is 15. So, multiply each term by 15:

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

Simplifying:

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

### Step 2: Move all the terms involving \(x\) to one side and constant terms to the other side
Move the terms involving \(x\) to the left-hand side and constants to the right-hand side:

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

Simplifying:

\[
-16x = -40
\]

### Step 3: Solve for \(x\)
Now divide both sides by \(-16\):

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

Thus, the solution is:

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

Would you like more details on any step or further clarification?

### Relative Questions:
1. How do you find the least common denominator (LCD) for fractions?
2. Why do we move terms involving \(x\) to one side and constants to the other side?
3. How can you check your solution once you find \(x\)?
4. What happens if both sides of the equation contain fractions with different denominators?
5. Can you solve this equation using a different method?

### Tip:
When working with equations that have fractions, multiplying by the least common denominator helps eliminate fractions and simplify the problem.

Learn how to solve the linear equation with fractions: -2/5x + 3 = 2/3x + 1/3. This step-by-step solution includes clearing fractions using the least common denominator and solving for x. Suitable for students in Grades 8-10.

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