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Algebra II Recipe: Solving Linear Equations
A. Steps for Solving
  1. Do the distributive property on each side.
  2. Combine like terms on each side.
  3. Add or subtract to get the variable terms on the same side. The side of the largest coefficient is best.
  4. Add or subtract to move the number term to the opposite side of the variable term.
  5. Multiply or divide to move the coefficient to the opposite side of the variable term.
ExamplesExamples:
7x - 29 = -15
x - 30 = 6 - 2x
4(-3x + 1) = -10(x - 4) - 14x
-4(3 + x) + 5 = 4(x + 3)
B. Solving Equations with Fraction
  1. Multiply each term in the equation by the LCD.
  2. Collect like terms and follow the steps above in part A.
ExamplesExample:
(1/3)x + (1/4) = x - (1/6)
C. Solving Equations with Decimals
  1. Multiply each term in the equation by 10, 100, or 1,000 to make all numbers whole.
    • Only numbers on the outside of parentheses get multiplied by the 10, 100, or 1,000.
  2. Collect like terms and follow the steps above in part A.
ExamplesExample:
3.1(x + 2) - 1.5x = 5.2(x - 4)
D. If the Variable Terms Cancel on Both Sides of the Equation:
  1. The answer is No Solution, if a false statement is the result.
  2. The answer is All Real Numbers, if a true statement is the result.
ExamplesExample:
3(x - 1) = 5x + 3 - 2x



G Redden

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