2

(

3

h

+

9

)

=

3

(

–

2

h

+

10

)

Let's solve the equation:

\[
2(3h + 9) = 3(-2h + 10)
\]

### Step 1: Distribute the \(2\) on the left side and the \(3\) on the right side.

\[
2 \times 3h + 2 \times 9 = 3 \times (-2h) + 3 \times 10
\]

This simplifies to:

\[
6h + 18 = -6h + 30
\]

### Step 2: Add \(6h\) to both sides to get all the \(h\) terms on one side of the equation.

\[
6h + 6h + 18 = 30
\]

This simplifies to:

\[
12h + 18 = 30
\]

### Step 3: Subtract 18 from both sides to isolate the \(h\) term.

\[
12h = 30 - 18
\]

This simplifies to:

\[
12h = 12
\]

### Step 4: Divide both sides by 12 to solve for \(h\).

\[
h = \frac{12}{12}
\]

This simplifies to:

\[
h = 1
\]

So, the solution is \(h = 1\).

Would you like more details on any part of this solution?

Here are 5 related questions you might be interested in:
1. How do you solve equations involving distribution and combining like terms?
2. What are the steps to isolate the variable in an equation?
3. How do you handle equations with both positive and negative coefficients?
4. What are the methods to verify your solution to an equation?
5. How do you solve equations with variables on both sides more efficiently?

**Tip:** Always remember to perform the same operation on both sides of the equation to maintain equality.

Learn how to solve the equation 2(3h + 9) = 3(-2h + 10) step-by-step with a detailed solution. This problem covers equations involving distribution and combining like terms. Suitable for students in Grades 7-9.

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