Identify the simplest form of the expression 2(x + 3) + 4(x - 1).

Identify the simplest form of the expression 2(x + 3) + 4(x - 1).

• A. 6x + 2
• B. 6x + 10
• C. 4x + 6
• D. 4x + 10

Answer: (B)

To simplify the expression 2(x + 3) + 4(x - 1), you first need to distribute the coefficients to the terms inside the parentheses. Starting with 2(x + 3), distribute the 2: - 2 * x = 2x - 2 * 3 = 6 This gives you 2x + 6. Next, for 4(x - 1), distribute the 4: - 4 * x = 4x - 4 * -1 = -4 This results in 4x - 4. Now, combine the results from the two distributions: 2x + 6 + 4x - 4. Next, combine like terms: - Combine the x terms: 2x + 4x = 6x - Combine the constant terms: 6 - 4 = 2 When you put it all together, the expression simplifies to 6x + 2, which is the simplest form. This means the correct answer is 6x + 2, which directly matches the option provided. The misunderstanding might have arisen in the calculation or when identifying the output of combining like terms.

To simplify the expression 2(x + 3) + 4(x - 1), you first need to distribute the coefficients to the terms inside the parentheses.

Starting with 2(x + 3), distribute the 2:

• 2 * x = 2x

• 2 * 3 = 6

This gives you 2x + 6.

Next, for 4(x - 1), distribute the 4:

• 4 * x = 4x

• 4 * -1 = -4

This results in 4x - 4.

Now, combine the results from the two distributions:

2x + 6 + 4x - 4.

Next, combine like terms:

• Combine the x terms: 2x + 4x = 6x

• Combine the constant terms: 6 - 4 = 2

When you put it all together, the expression simplifies to 6x + 2, which is the simplest form.

This means the correct answer is 6x + 2, which directly matches the option provided. The misunderstanding might have arisen in the calculation or when identifying the output of combining like terms.