Solution of Equation - Solving More Complex Equations

Most equations are given in a more complicated form which can be simplified. Consider the equation 4x - x - 5 = 2x + 7. The first step in solving this equation is to combine like terms on each side of the equation. On the right side there are no like terms, but the 4x and -x on the left side are like terms. This equation, when simplified, becomes 3x - 5 = 2x + 7. The next step is to eliminate the unknown from one side of the equation. For this example, this is accomplished by adding -2x to both sides of the equation, which gives x - 5 = 7. Using the additive property, the solution is obtained by adding 5 to both sides of the equation, so x = 12.

The whole process for solving single variable algebraic equations can be summarized by the following steps. First, eliminate any parentheses by multiplying out factors. Second, add the like terms in each side. Third, eliminate the unknown from one side of the equation using the multiplicative or additive properties. Fourth, eliminate the constant term from the side with the unknown using the additive property. Finally, eliminate any coefficient on the unknown by using the multiplicative property.