Section 3.4: Equations
Essential Ideas
  • Equation
    An equation is a statement of equality between two expressions called the left side and the right side. There are three types of equations: true, false, and open. An open (or conditional) equation is an equation which depends on the value of a variable. Values that make the conditional equation true are called the solution or roots of the equation and are said to satisfy the equation.

  • To solve an equation means to find the replacement for the unknown (that is, the variable or variables), that makes the equation true.

  • Two numbers whose sum is 0 are called opposites.
    Two numbers whose product is 1 are called reciprocals.

  • Property of Equations
    The solution of an equation is unchanged by adding the same number to both sides of the equation subtracting the same number from both sides of the equation multiplying both sides of the equation by the same nonzero number dividing both sides of the equation by the same nonzero number.