Which equation is equivalent to 3 + 5(x + 2) = 12?

Question

A. 8x + 16 = 12

B. 8x + 2 = 12

C. 5x + 5 = 12

D. 5x + 13 = 12

Answer 1

To find an equivalent equation to \(3 + 5(x + 2) = 12\), we need to simplify the left side of the equation.

1. Start with the original equation: \[ 3 + 5(x + 2) = 12 \]

2. Distribute \(5\) to both terms inside the parentheses: \[ 3 + 5x + 10 = 12 \]

3. Combine the constants on the left side: \[ (3 + 10) + 5x = 12 \] \[ 13 + 5x = 12 \]

Now, we can rewrite the equation as: \[ 5x + 13 = 12 \]

Thus, the equivalent equation is: \[ \boxed{D. , 5x + 13 = 12} \]