We start by solving the equation:

\[
(x + 9)\frac{3}{5} + 7 = 15
\]

### Step 1: Isolate the term with \( x \)
First, subtract 7 from both sides to get rid of the constant on the left-hand side:

\[
(x + 9)\frac{3}{5} = 15 - 7
\]

Simplifying the right-hand side:

\[
(x + 9)\frac{3}{5} = 8
\]

### Step 2: Eliminate the fraction
To eliminate the fraction \(\frac{3}{5}\), multiply both sides of the equation by the reciprocal of \(\frac{3}{5}\), which is \(\frac{5}{3}\):

\[
x + 9 = 8 \times \frac{5}{3}
\]

Simplifying the right-hand side:

\[
x + 9 = \frac{40}{3}
\]

### Step 3: Isolate \( x \)
Now, subtract 9 from both sides:

\[
x = \frac{40}{3} - 9
\]

We need to express 9 as a fraction with denominator 3:

\[
x = \frac{40}{3} - \frac{27}{3}
\]

Simplifying:

\[
x = \frac{40 - 27}{3} = \frac{13}{3}
\]

### Final Answer:
\[
x = \frac{13}{3}
\]

Would you like a detailed explanation of any steps or more practice problems? Here are some related questions:

1. How would you solve \( (x - 4)\frac{2}{3} + 5 = 12 \)?
2. What happens if we replace \( \frac{3}{5} \) with \( \frac{4}{5} \) in the original equation?
3. How do you solve an equation involving more complex fractions, like \( (x + 2)\frac{5}{6} + 3 = 10 \)?
4. How can you verify your answer once you've solved for \( x \)?
5. How would the solution change if the original equation were \( (x + 9)\frac{3}{5} - 7 = 15 \)?

**Tip:** Always aim to isolate the variable step by step, simplifying as much as possible at each stage.

Learn how to solve the linear equation (x + 9)3/5 + 7 = 15 step-by-step, focusing on key algebraic concepts like isolating variables and handling fractional coefficients. Suitable for students in Grades 6-8.

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