Let's solve the equation step by step:

The given equation is:

\[
2(h + 1) = 5h - 7
\]

### Step 1: Distribute the 2 on the left side.
\[
2h + 2 = 5h - 7
\]

### Step 2: Move all terms involving \( h \) to one side and constants to the other side.
Subtract \( 2h \) from both sides:
\[
2 = 5h - 2h - 7
\]
\[
2 = 3h - 7
\]

### Step 3: Isolate \( h \) by adding 7 to both sides.
\[
2 + 7 = 3h
\]
\[
9 = 3h
\]

### Step 4: Solve for \( h \) by dividing both sides by 3.
\[
h = \frac{9}{3} = 3
\]

So, the solution is:
\[
h = 3
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What happens when you distribute numbers in equations?
2. How can you check if the solution to an equation is correct?
3. What are the different ways to solve for a variable in linear equations?
4. How do you solve equations with variables on both sides?
5. Can you explain what it means to isolate the variable in an equation?

**Tip:** Always double-check your solution by substituting the variable back into the original equation.

Learn how to solve the linear equation 2(h+1)=5h-7 step by step, including applying the distributive property and isolating the variable h. Suitable for students in Grades 6-8, this problem covers essential algebraic concepts.

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