Which is a reasonable first step that can be used to solve the equation 4 x + 3 (x + 2) = 5 (2 x minus 3)?

Question

Distribute the 3 to x + 2, and distribute the 5 to (2x – 3).
Combine 4x and x on the left side of the equation.
Apply the subtraction property of equality to move the 2 from the left to the right side of the equation.
Apply the addition property of equality to move the 3 from the right to the left side of the equation.

Answer 1

To solve the equation $4x+3(x+2)=5(2x-3)$, a reasonable first step would be to distribute the constants across the terms in the parentheses. Specifically, this involves distributing the 3 to $x+2$ on the left side and distributing the 5 to $2x-3$ on the right side.

Therefore, the correct step is:

Distribute the 3 to $x+2$, and distribute the 5 to $(2x-3)$.

Once the distributions are done, the equation can be simplified further and solved for $x$.