To solve the equation \( 0 = -\frac{7}{3}x + \frac{5}{3} \), we need to isolate \( x \). Here's the step-by-step process:

### Step 1: Eliminate the fractions
Multiply the entire equation by 3 to get rid of the denominators:
\[
3 \times 0 = 3 \times \left(-\frac{7}{3}x + \frac{5}{3}\right)
\]
\[
0 = -7x + 5
\]

### Step 2: Isolate the variable term
Subtract 5 from both sides:
\[
0 - 5 = -7x
\]
\[
-5 = -7x
\]

### Step 3: Solve for \( x \)
Divide both sides by -7:
\[
x = \frac{-5}{-7}
\]
\[
x = \frac{5}{7}
\]

### Final Answer:
\[
x = \frac{5}{7}
\]

Would you like any further explanation on this, or do you have any additional questions?

### Relative questions:
1. How do you solve linear equations with fractions?
2. What is the general method to isolate variables in algebraic equations?
3. How do you handle negative coefficients when solving equations?
4. Can you show how to check if \( x = \frac{5}{7} \) is the correct solution by plugging it back into the original equation?
5. What other methods can be used to solve linear equations besides isolating variables?

### Tip:
Always double-check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

Learn how to solve the linear equation 0 = -7/3x + 5/3 in this step-by-step guide. This solution demonstrates how to eliminate fractions, isolate variables, and handle negative coefficients, suitable for students in Grades 8-10.

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