https://file.aiquickdraw.com/mathbot/file/1727451280993huk951b7.jpg

The given equation is:

\[
\frac{2}{3}(6h - 12) = \frac{3}{4}(4h + 20)
\]

Let's solve it step-by-step.

### Step 1: Distribute the fractions
First, distribute \(\frac{2}{3}\) and \(\frac{3}{4}\) to the terms inside the parentheses.

\[
\frac{2}{3} \cdot 6h - \frac{2}{3} \cdot 12 = \frac{3}{4} \cdot 4h + \frac{3}{4} \cdot 20
\]

\[
4h - 8 = 3h + 15
\]

### Step 2: Isolate \(h\)
Subtract \(3h\) from both sides:
\[
4h - 3h - 8 = 15
\]
\[
h - 8 = 15
\]

Add 8 to both sides:
\[
h = 23
\]

### Solution
The solution to the equation is:
\[
h = 23
\]

Would you like a more detailed explanation or have any further questions?

### Related Questions:
1. How do you handle equations with fractions more generally?
2. What happens if there's a variable in the denominator?
3. How do you verify the solution to such an equation?
4. Can you solve similar equations with different coefficients?
5. What are some strategies to solve equations involving multiple fractions?

**Tip:** Always clear fractions early by multiplying by the least common multiple (LCM) if it simplifies the equation.

What is the solution to the equation \( \frac{2}{3}(6h - 12) = \frac{3}{4}(4h + 20) \)?

Learn how to solve the linear equation \( \frac{2}{3}(6h - 12) = \frac{3}{4}(4h + 20) \) with a detailed step-by-step solution. This problem demonstrates the distributive property, solving linear equations, and handling fractions. Suitable for students in Grades 8-10.

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