To solve the equation \( 15 = \frac{3}{4}(9x + 8) \), follow these steps:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 4 to get rid of the denominator:
\[
4 \times 15 = 4 \times \frac{3}{4}(9x + 8)
\]
This simplifies to:
\[
60 = 3(9x + 8)
\]

### Step 2: Distribute the 3 on the right-hand side
Distribute the 3 to both terms inside the parentheses:
\[
60 = 27x + 24
\]

### Step 3: Isolate the variable \(x\)
Subtract 24 from both sides to move constants to one side:
\[
60 - 24 = 27x
\]
\[
36 = 27x
\]

### Step 4: Solve for \(x\)
Divide both sides by 27 to isolate \(x\):
\[
x = \frac{36}{27}
\]
Simplify the fraction:
\[
x = \frac{4}{3}
\]

### Final Answer:
\[
x = \frac{4}{3}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve equations with different fractions?
2. What happens when the variable is inside parentheses in an equation?
3. How do you simplify complex fractions?
4. How can you check if your solution for \(x\) is correct?
5. What other methods can be used to solve linear equations?

**Tip:** Always try to eliminate fractions early in the process by multiplying both sides of the equation by the denominator.

Learn how to solve the linear equation 15 = 3/4(9x + 8) with a step-by-step breakdown. This problem involves distributing and eliminating fractions, core algebra concepts suitable for students in Grades 8-10.

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