How to Solve Algebra Linear Equations

A linear equation consists of constants and variables to the first power. There can be more than a single variable in a linear equation, but they must all be to the first power. If it is not to the first power, it is a nonlinear equation. Linear equations are usually the simplest to solve.

Things You'll Need

• Linear equation
• Paper
• Pencil

Instructions

1. Take a look at the equation and make sure it is linear. Remember all variables should be to the first power. In this example, use 2(x + 3) - (x + 4) = -2(x + 3) + 11.

2. Multiply through the factors to get rid of the parentheses. In the example, this results in 2x + 6 - x - 4 = -2x - 6 + 11.

3. Group all the like terms by performing the addition and subtraction operations as required by the order of operations. In this example, the result is x + 2 = -2x + 5.

4. Get all the common terms on the same side. For this example, add 2x to both sides and subtract 2 from both sides. This will yield 3x = 3.

5. The final step is to solve for x. For this example, divide both sides by 3. This gives x = 1.

Tips & Warnings

• Make sure you are solving a linear equation.

• Watch your arithmetic, especially the multiplication of negatives.

References

• PurpleMath: Solving One-Step Linear Equations
• Algebra.com: Linear Equation and System Solvers