How to Solve Linear Equations by Combining Like Terms
- 1). Determine a linear equation to solve. A linear equation contains variables raised only to the power of 1. For the following example, use the equation 4x + 3 - x = 2x + 4 + 1.
- 2). Combine the like terms on the left side of the equation by adding or subtracting. In the example, 4x and -x are like terms, so subtract x from 4x. This equals 3x, which leaves 3x + 3 = 2x + 4 + 1.
- 3). Combine the like terms on the right side of the equation by adding or subtracting. In the example, the numbers 4 and 1 are like terms because they are both constants, so add 4 to 1. This equals 5, which leaves 3x + 3 = 2x + 5.
- 4). Add or subtract the term with a variable on the ride side of the equation to both sides of the equation to isolate the terms with variables on the left side of the equation. In the example, subtract 2x from both sides of the equation. This results in 3x + 3 - 2x = 2x + 5 - 2x.
- 5). Combine the like terms with variables on the left side of the equation and eliminate the terms with variables on the right side of the equation. In the example, subtract 2x from 3x on the left side of the equation and subtract 2x from 2x on the right side of the equation. This leaves x + 3 = 5.
- 6). Add or subtract the number on the left side of the equation to both sides of the equation to eliminate it from the left side of the equation and isolate the variable on the left side of the equation. In the example, subtract 3 from both sides of the equation, which results in x + 3 - 3 = 5 - 3.
- 7). Combine the like terms on the right side of the equation and eliminate the numbers on the left side of the equation. In the example, subtract 3 from 5 on the right side of the equation, and subtract 3 from 3 on the left side. This leaves x = 2, which is the solution to the equation.