# Math - Solve Equation

by David
(Newark, NJ, USA)

how do I solve 5 - 2(x - 1) = 12 I want to solve for x

### Comments for Math - Solve Equation

 Dec 30, 2011 Solve Equation by: Staff Question: by David (Newark, NJ, USA) how do I solve 5 - 2(x - 1) = 12 I want to solve for x Answer: 5 - 2(x - 1) = 12 Eliminate the parentheses on the left side of the equation using the distributive law. 5 + (- 2)*(x - 1) = 12 5 + (- 2)*x + (- 2)*(- 1) = 12 5 - 2x + 2 = 12 Combine like terms on the left side of the equation. (The Commutative Property of Addition states that any two addends can be added in either order without changing the results. Therefore: - 2x + 2 = 2 - 2x ) 5 - 2x + 2 = 12 5 + 2 - 2x = 12 (5 + 2) - 2x = 12 (7) - 2x = 12 7 - 2x = 12 Add 2x to each side of the equation. 7 - 2x + 2x = 12 + 2x 7 + 0 = 12 + 2x 7 = 12 + 2x Subtract 12 from each side of the equation 7 - 12 = 12 + 2x - 12 7 - 12 = 12 - 12 + 2x 7 - 12 = 0 + 2x 7 - 12 = 2x -5 = 2x Divide each side of the equation by 2 -5/2 = 2x/2 -5/2 = x*(2/2) -5/2 = x*(1) -5/2 = x x = -5/2 the final answer is: x = -5/2 Check the final answer by substituting -5/2 for x in the original equation: 5 - 2(x - 1) = 12 5 - 2(-5/2 - 1) = 12 5 + 5 + 2 = 12 12 = 12, OK → x = -5/2 is a VALID solution Thanks for writing. Staff www.solving-math-problems.com