You have the equation:

\[
\frac{2}{7}x - \frac{2}{3} = 2
\]

Let's solve for \(x\) step by step:

### Step 1: Eliminate the fraction \(\frac{2}{3}\) on the left side
Add \(\frac{2}{3}\) to both sides:

\[
\frac{2}{7}x = 2 + \frac{2}{3}
\]

### Step 2: Find a common denominator to add the fractions on the right
The least common denominator (LCD) between 2 and \(\frac{2}{3}\) is 3. Express 2 as a fraction with denominator 3:

\[
2 = \frac{6}{3}
\]

Now add the fractions:

\[
\frac{2}{7}x = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}
\]

### Step 3: Eliminate the fraction \(\frac{2}{7}\) by multiplying both sides by the reciprocal of \(\frac{2}{7}\), which is \(\frac{7}{2}\):

\[
x = \frac{8}{3} \times \frac{7}{2}
\]

### Step 4: Multiply the fractions:

\[
x = \frac{8 \times 7}{3 \times 2} = \frac{56}{6}
\]

### Step 5: Simplify the fraction:

\[
x = \frac{28}{3}
\]

Thus, the solution is:

\[
x = \frac{28}{3}
\]

Would you like more details on any step or have questions?

### Related Questions:
1. How do you solve equations with more complex fractions?
2. Can we convert fractions to decimals when solving?
3. How does cross-multiplication work in equations like this?
4. What happens when the equation involves mixed fractions?
5. How do you solve an equation when both sides are fractions?

### Tip:
When solving equations with fractions, finding a common denominator or multiplying through by the least common denominator helps eliminate fractions early on for a cleaner solution.

Learn how to solve the linear equation 2/7(x) - 2/3 = 2 step-by-step. This problem involves key algebraic concepts such as fraction addition and multiplication, suitable for students in Grades 6-8.

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