https://file.aiquickdraw.com/mathbot/file/17267939545128ze436o6.jpg

The equation from the image is:

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

Let's solve it step by step:

1. Combine like terms. The terms involving \(x\) are \(\frac{5}{9}x\) and \(-\frac{1}{3}x\). To combine them, we need a common denominator. The least common denominator between 9 and 3 is 9. So, rewrite \(-\frac{1}{3}x\) as \(-\frac{3}{9}x\).

Now the equation looks like:
\[
\frac{5}{9}x - \frac{3}{9}x - 1 = 3
\]

2. Combine the \(x\)-terms:
\[
\left(\frac{5}{9}x - \frac{3}{9}x\right) = \frac{2}{9}x
\]
Now the equation becomes:
\[
\frac{2}{9}x - 1 = 3
\]

3. Add 1 to both sides to move the constant term to the right side:
\[
\frac{2}{9}x = 4
\]

4. To solve for \(x\), multiply both sides by the reciprocal of \(\frac{2}{9}\), which is \(\frac{9}{2}\):
\[
x = 4 \times \frac{9}{2}
\]

5. Simplify:
\[
x = \frac{36}{2} = 18
\]

So, the solution is:
\[
x = 18
\]

Would you like further details or have any questions? Here are some related questions:

1. How do you find the least common denominator when combining fractions?
2. Why is it important to combine like terms in an equation?
3. How do you solve equations that involve fractions and constants?
4. What happens if you multiply both sides of an equation by the reciprocal of a fraction?
5. How can checking your solution help ensure accuracy in solving equations?

**Tip:** When solving equations with fractions, it's often helpful to clear the denominators by multiplying through by the least common denominator!

Solve the following equation: (5/9)x - 1 - (1/3)x = 3

Learn how to solve a multi-step equation involving fractions: (5/9)x - 1 - (1/3)x = 3. This detailed solution walks through combining like terms, finding a common denominator, and solving linear equations with fractions. Suitable for Grades 8-10 students.

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