5 Steps to Solving Linear Equations in One Variable
1. Simplify each side of the equation by removing any grouping symbols
with the distributive property.
2. Combine like terms on each side of the equation.
3. Use the Additive Property of Equality to add the opposite of the constant
term and/or variable term to both sides of the equation so that the
variables are isolated on one side of the equation and the constants are
isolated on the other side of the equation.
4. Use the Multiplication Property of Equality to multiply both sides of the
equation by the reciprocal of the coefficient of the variable (or divide
both sides by the coefficient itself). Note: the coefficient of the variable
will become +1.
5. Check you answer by substituting your solution into the original
equation and simplify. Note: if your answer is a solution, then both sides
of the equation will be equal.
Example 1: 3x – 2 = 7
3x – 2 + 2 = 7 + 2
3x = 9
(3x) = (9)
+1x = x = 3
Example 2: 2 (x+5) = 30
2x +10 = 30
2x +10 – 10 = 30 – 10
2x = 20
(2x) = (20)
+1x = x = 10
Example 3: 6(x+2) – 4 = 2(x – 3) – 2
6x + 12 – 4 = 2x – 6 – 2
6x + 8 = 2x – 8
6x + 8 – 8 = 2x – 8 – 8
6x = 2x – 16
6x – 2x = 2x – 2x – 16
4x = -16
(4x) = (-16)
+ 1 x = x = -4