The expression 3(2x + 7) − 4(−3x + 5) is equal (=) to
Responses
A	18x + 118x + 1
B	18x + 2718x + 27
C	18x + 1618x + 16
D	− 6x + 1− 6x + 1
E	− 6x + 27

Let's simplify the given expression step by step:

### Expression:
\[
3(2x + 7) - 4(-3x + 5)
\]

### Step 1: Distribute the constants inside the parentheses.
- Distribute **3** to both \(2x\) and \(7\):
  \[
  3(2x) + 3(7) = 6x + 21
  \]
- Distribute **-4** to both \(-3x\) and \(5\):
  \[
  -4(-3x) + (-4)(5) = 12x - 20
  \]

### Step 2: Combine the results from both distributions.
\[
6x + 21 + 12x - 20
\]

### Step 3: Combine like terms.
- Combine the \(x\)-terms: \(6x + 12x = 18x\)
- Combine the constant terms: \(21 - 20 = 1\)

### Final simplified expression:
\[
18x + 1
\]

### Answer:
The correct response is:
\[
\boxed{A \, 18x + 1}
\]

Do you want more details or have any questions?

### Related Questions:
1. How would the solution change if the constants were different?
2. What happens if we had a subtraction instead of addition in one of the parentheses?
3. How can we verify that the result is correct?
4. What role does the distributive property play in solving this?
5. How do like terms affect the simplification process?

### Tip:
When dealing with expressions that involve distribution, always remember to distribute both the sign and the number to avoid mistakes.

The expression 3(2x + 7) − 4(−3x + 5) is equal (=) to

Learn how to simplify the algebraic expression 3(2x + 7) - 4(-3x + 5) using the distributive property and combining like terms. This step-by-step solution is suitable for students in Grades 7-9, covering key algebraic concepts like distribution and simplifying expressions.

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