AlgebraLab

Algebra I Recipe: Solving One-Step Equations

By G Redden

A. Quick Facts and Definitions:
  1. When solving an equation, the goal is to get the variable by itself on one side of the equation.
  2. Inverse operations are the same as opposite operations.
  3. Addition and subtraction are inverse operations.
  4. Multiplication and division are inverse operations.
  5. variable term – the term containing a variable.
  6. number term – the term containing only a number.
B. Given an equations like x + 2 = 10 and x - 5 = 12
  1. If the number term is positive, subtract it from both sides of the equation.
  2. If the number term is negative, add its positive value to both sides of the equation.

x + 5 = 10

t – 2 = 6

11 = r – 4

–9 = 2 + y

n – 5 = -9

–3 + x = 7

C. Given equations like: 2x = 10,    x/-3 = 10,    ¾x = 10
  1. If the coefficient is an integer, then divide by that number on both sides of the equation.
  2. If the variable is being divided by an integer, multiply by that number on both sides of the equation.
  3. If the coefficient is a fraction, multiply by the reciprocal of the fraction on both sides of the equation.

–21m = 42

30b = 5

288 = 16t

8x = 3

y/7 = 12

m/-4 = -¾

z/2 = -5

(-4/5)x = 72

(-2/3)t = -16

¾z = -5½

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