3 Like TermsTerm- a number, variable, or product of a number and one or more variablesEx.: 3a – 4b + 5 has 3 termsLike Terms- terms with the same variables and the same exponentsEx.: 2x, 3x4mn, 12mnIn the term 3a, 3 is calledthe numerical coefficientNote:and areNOT like terms
8 Solving EquationsIn this section we are going to learn how to solve linear (or first degree) equations.A linear equation is one in which the exponent on the variable is 1.Example: 5x – 1 = 32x + 4 = 6x - 5
9 Equivalent EquationsEquivalent Equations are equations that have the same solution.The following are equivalent equations:2x – 5 = 12x = 6x = 3
10 When we solve an equation, we write the equation as a series of simpler equivalent equations until we obtain an equation of the form x = c, where c is some real number.
11 Isolate the VariableTo solve any equation, we have to isolate the variable.That means getting the variable by itself on one side of the equals sign.There are 4 properties we will use to isolate the variable.
12 Addition Property of Equality You can add the same number to bothsides of an equation and the equationremains equivalent.
20 Procedure to Solve Equations 1. Get rid of fractions.2. Distribute when needed.3. Combine like terms on same side of equals.Use the addition/subtraction property. Youmay have to use it more than once!Solve using either the multiplication propertyor the division property.
24 Variables on Both Sides Your goal is to get the variable on one side of the equals sign and everything else on the other side of the equals sign.Always combine like terms on each side of the equation FIRST!