Let's solve the equation step by step:

\[
5(2x + 1) + 5x - 2 = 48
\]

1. **Distribute** the \(5\) to the terms inside the parentheses:

\[
10x + 5 + 5x - 2 = 48
\]

2. **Combine like terms** on the left side:

\[
15x + 3 = 48
\]

3. **Subtract 3** from both sides to isolate the terms with \(x\):

\[
15x = 45
\]

4. **Divide by 15** to solve for \(x\):

\[
x = 3
\]

The solution is \(x = 3\).

Would you like further details on any of these steps, or do you have another question?

Here are some related questions you might find interesting:
1. How would you solve the equation \(4(3x - 2) + 2x = 18\)?
2. What are some strategies for solving equations with distribution, like \(7(2x + 4) = 28\)?
3. How do you solve an equation where the variable appears on both sides, like \(6x - 4 = 2x + 8\)?
4. What happens if you factor out a common factor from an equation before solving it?
5. Can you solve the equation \(3x + 5 = 5x - 7\)? How is this similar or different?

**Tip:** When distributing a constant across a binomial, ensure each term inside the parentheses is multiplied correctly to avoid errors later in the solution process.

Learn how to solve the equation 5(2x + 1) + 5x - 2 = 48 step-by-step with a detailed solution. This problem covers key algebraic concepts including equations, distributive property, and solving equations. Suitable for students in Grades 7-9.

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