Let's expand and simplify the expression:

\[
4(2x - 1) + 3(2x + 5)
\]

1. Distribute the \(4\) to both terms inside the first parentheses:

\[
4 \times 2x = 8x \quad \text{and} \quad 4 \times -1 = -4
\]

So, \(4(2x - 1)\) becomes:

\[
8x - 4
\]

2. Now, distribute the \(3\) to both terms inside the second parentheses:

\[
3 \times 2x = 6x \quad \text{and} \quad 3 \times 5 = 15
\]

So, \(3(2x + 5)\) becomes:

\[
6x + 15
\]

Now, putting everything together:

\[
8x - 4 + 6x + 15
\]

3. Combine like terms:

\[
(8x + 6x) = 14x \quad \text{and} \quad (-4 + 15) = 11
\]

Thus, the simplified expression is:

\[
14x + 11
\]

Would you like more details or have any other questions? Here are some related questions to explore further:

1. How do you handle distribution when multiplying binomials?
2. What are the steps to solve an equation after expanding expressions?
3. Can you simplify expressions involving more than two terms?
4. What is the distributive property, and how is it applied in algebra?
5. How would you solve for \(x\) in an equation involving this expression?

**Tip**: Always combine like terms after expanding to make your expression as simple as possible.

Learn how to expand and simplify the algebraic expression 4(2x-1) + 3(2x+5) with a detailed step-by-step explanation. This problem involves applying the distributive property and combining like terms, making it ideal for students in Grades 6-8.

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