https://file.aiquickdraw.com/mathbot/file/1726448728671xn22c2ti.jpg

The equation shown in the image is:

\[
\frac{x}{9} - \frac{2}{5} = \frac{1}{3}
\]

Let's solve for \( x \).

### Step 1: Eliminate the fractions
To eliminate the fractions, we can multiply through by the least common denominator (LCD) of 9, 5, and 3, which is 45.

Multiplying both sides of the equation by 45:

\[
45 \cdot \left( \frac{x}{9} \right) - 45 \cdot \left( \frac{2}{5} \right) = 45 \cdot \left( \frac{1}{3} \right)
\]

This simplifies to:

\[
5x - 18 = 15
\]

### Step 2: Solve for \( x \)

Now, add 18 to both sides:

\[
5x = 15 + 18
\]

\[
5x = 33
\]

Finally, divide both sides by 5:

\[
x = \frac{33}{5}
\]

Thus, the solution is:

\[
x = \frac{33}{5} \quad \text{or} \quad x = 6.6
\]

---

Would you like more details on any of the steps?

Here are 5 related questions you can explore:

1. How do you solve equations with multiple fractions like this?
2. What is the significance of finding the least common denominator (LCD)?
3. How can we check the solution by substituting back into the original equation?
4. What other methods can be used to eliminate fractions in equations?
5. Can this type of equation be solved graphically?

**Tip:** Always simplify fractions or expressions where possible before solving equations to make the process easier.

Learn how to solve the equation x/9 - 2/5 = 1/3 by eliminating fractions. This step-by-step solution covers key algebraic concepts, including multiplying through by the least common denominator (LCD) and solving for x. Suitable for students in Grades 7-9.

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