Unit 2 - Objective 4 - Solving First Degree Equations

An equation is an algebraic statement. It asserts that two algebraic expressions are equal. An equation that is true for only some values of the variables and not true for the other values is a conditional equation. For example 4x = - 24 is true only when x = - 6. To solve an equation we find the values of the unknown that satisfies it. You must perform the same operation on both sides of the equations.

Operations for changing equations into equivalent equations:

  1. Add or subtract the same amount to both sides of the equation
  2. Multiply or divide both sides of the equation by the same amount provided you do not divide both sides by 0.


    1. x + 7 = 15
    x + 7 - 7 = 15 - 7 (subtract 7 from both sides of the equation)
    x = 8
    2. 3x = 15
    (divide both sides of the equation by 3)
    x = 5

Not all equations are this easy so we must have some procedures for solving equations.

Procedures for Solving Equations

  1. Eliminate fractions. Multiply both sides of the equation by a common denominator (This step is optional but highly recommended).
  2. Remove grouping symbols. Perform the indicated multiplications and remove parenthesis, brackets, and braces.
  3. Combine like terms wherever possible.
  4. Get all terms containing the variable on one side of the equation. All other terms should be placed on the other side of the equation.
  5. Divide both sides by the coefficient of the variable. (You may have to factor the variable to see the coefficient)
  6. Check your answer in the original equation (optional).



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