To solve the equation \( \frac{2}{x} - 7 = \frac{10}{9} \), we will go step by step:

### Step 1: Isolate the fraction term
Add 7 to both sides of the equation to move the constant term:
\[
\frac{2}{x} = \frac{10}{9} + 7
\]
Convert 7 to a fraction with a denominator of 9:
\[
\frac{2}{x} = \frac{10}{9} + \frac{63}{9}
\]
Now, add the fractions:
\[
\frac{2}{x} = \frac{73}{9}
\]

### Step 2: Solve for \( x \)
To isolate \( x \), multiply both sides of the equation by \( x \) and then divide by \( \frac{73}{9} \):
\[
2 = \frac{73}{9}x
\]
Multiply both sides by \( \frac{9}{73} \) to solve for \( x \):
\[
x = \frac{2 \times 9}{73} = \frac{18}{73}
\]

So, the solution is:
\[
x = \frac{18}{73}
\]

Would you like more details or have any questions?

Here are 5 related questions you might want to explore:
1. How do you solve other equations involving fractions?
2. What happens if the fractions have different denominators?
3. How do you solve equations with variables in the denominator?
4. How can you check if your solution is correct?
5. How does cross-multiplication work in equations like this?

**Tip:** Always simplify fractions before solving to make the calculation easier.

Discover how to solve the algebraic equation 2/x - 7 = 10/9 with a detailed, step-by-step breakdown. This problem focuses on key algebraic concepts such as manipulating equations with fractions and cross multiplication. Ideal for students in Grades 8-10.

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