Question

Question

Which expression is equivalent to 2(x+3)+4(x+1)
?(1 point)
Responses

3x+10
3 x plus 10

2x+10
2 x plus 10

6x+10
6 x plus 10

6x+7

Answer 1

To simplify the expression \( 2(x+3) + 4(x+1) \), we'll distribute the constants across the terms inside the parentheses:

1. Distribute \( 2 \) to \( (x + 3) \): \[ 2(x + 3) = 2x + 6 \]

2. Distribute \( 4 \) to \( (x + 1) \): \[ 4(x + 1) = 4x + 4 \]

Now, we can combine these results: \[ 2x + 6 + 4x + 4 \]

Next, combine the like terms \( 2x \) and \( 4x \): \[ 2x + 4x = 6x \]

Now, combine the constant terms \( 6 \) and \( 4 \): \[ 6 + 4 = 10 \]

Putting it all together, we have: \[ 6x + 10 \]

So, the expression equivalent to \( 2(x+3) + 4(x+1) \) is: \[ \boxed{6x + 10} \]

Thus, the correct response is 6x + 10.