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 \(x\).