Basic Algebra! (Solving Equations for One Unknown Variable) In the course of this semester, we will be learning about many simple relationships in nature. We will be working with equations that express the Precise Mathematical Relationship (PMR) between different variables. We will be problem-solving with these equations, so it is imperative that you become familiar with the appropriate means for manipulating them. You will need to be able to algebraically solve these equations for one unknown variable.

Think of an equation (PMR) as a perfectly balanced seesaw. The sides may not look the same, but the equal sign means that they must be! So, if you make a change to one side, you must make the same change to the other side to maintain the balance. Basic Algebra! (Solving Equations for One Unknown Variable)

General Rules of Thumb: Always isolate the term with the desired variable by adding or subtracting from both sides (if necessary). Solve for the desired variable in the term by performing inverse operations. Remember, whatever you do to one side of an equation must be done to the other side. (seesaw rule) Suggestion: Don’t do the algebra in your head or on the calculator – try to write down the algebra, THEN substitute numbers and units and THEN calculate the correct answer. This will help you avoid needless mathematical errors! Basic Algebra! (Solving Equations for One Unknown Variable)

Example: d = ½ a t 2 Solve for a:Solve for t: d = ½ a t 2 ½ t 2 a = d ½ t 2 2d 2d t 2 = d = ½ a t 2 ½ a t 2 = d ½ a t = 2d a √