Which expression is equivalent to 6A-3B, when A =  2x + 7 and B = 5x - 2?

Steps:

6(A)-3(B)

6(2x+7) - 3(5x - 2)

If the question is multiple choice, I can now check the answers in Desmos to see which answer gives me the same line.

Let's go through the steps you outlined:

We are given the expressions for \( A \) and \( B \):

- \( A = 2x + 7 \)
- \( B = 5x - 2 \)

We need to evaluate \( 6A - 3B \).

### Step-by-step solution:

1. **Substitute** the values of \( A \) and \( B \) into the expression \( 6A - 3B \):
   \[
   6(2x + 7) - 3(5x - 2)
   \]

2. **Distribute** the constants 6 and -3 to the terms inside the parentheses:
   \[
   6 \cdot 2x + 6 \cdot 7 - 3 \cdot 5x + 3 \cdot 2
   \]
   This simplifies to:
   \[
   12x + 42 - 15x + 6
   \]

3. **Combine like terms** (terms with \( x \) and constants):
   - \( 12x - 15x = -3x \)
   - \( 42 + 6 = 48 \)

So, the simplified expression is:
\[
-3x + 48
\]

This is the equivalent expression to \( 6A - 3B \).

If you're dealing with a multiple-choice question, you can now verify the correct option using a graphing tool like Desmos, comparing the linear expression \( -3x + 48 \) with the options provided.

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Do you want more details or have any questions?

Here are 5 related questions:
1. How can you solve the expression if it had higher powers of \( x \)?
2. What happens if the sign of \( A \) or \( B \) changes?
3. How do you handle expressions with more variables?
4. Can you factor the final expression \( -3x + 48 \)?
5. How would this process change with fractions instead of integers?

**Tip:** When combining terms, always double-check your signs to avoid simple mistakes.

Which expression is equivalent to 6A - 3B, when A = 2x + 7 and B = 5x - 2?

Learn how to simplify the expression 6A - 3B, where A = 2x + 7 and B = 5x - 2. This step-by-step solution covers the distributive property and combining like terms, suitable for students in Grades 8-10.

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