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How to Solve a Linear Equation Using the Two Equality Properties of Addition & Multiplication

A linear equation contains variables, or letters, representing unknown values, and constants, or numbers, combined with algebraic operations. When graphed, linear equations form straight lines. The purpose of a linear equation is to use algebra to isolate the variable on one side of the equation, thus solving for the variable and making all parts of the equation known. To properly solve an equation, the rules or properties of algebraic operations must be followed. The equality properties of addition and multiplication are two rules that commonly arise during the solution of a linear equation.

Instructions

- 1
  Solve a linear equation using the addition equality property, which states that if a = b than a + c = b + c, and the multiplication equality property, which states that if a = b then a(c) = b(c). Note that both of these properties simply state when an operation is performed to one side of an equation during solving, it needs to be applied to the other side of the equation to keep the equation equivalent.
- 2
  Solve the linear equation (1/2)x - 6 = 18 using the addition and multiplication properties. Eliminate the 6 from the side with the variable by adding a positive 6 to both sides of the equation: (1/2)x - 6 + 6 = 18 + 6 becomes (1/2)x = 24.
- 3
  Eliminate the (1/2) in (1/2)x = 24 by multiplying 2 to both sides: 2 * (1/2)x = 24 * 2 becomes (2/2)x = 48 or x = 48.

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