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Literal Equations Practice Foundations of Algebra Step 1. Start with an example. It could be an equation or a formula. Step 2. Identify the target variable. The first thing you need to do is identify what variable you are solving for, or your target variable. Your goal is to get all the letters in your equation on one side of the equation, and your target variable, by itself, on the other side of the equation. Step 3. Remember the order of operations. When solving literal equations, the order of operations is as follows: Exponents and roots, multiplication and division, addition and subtraction. When moving variables from one side of an equation to another you will perform the order of operations backwards: Subtraction, Addition, Division, Multiplication, Exponents, Parentheses. Step 4. Move the letters. Move all the letters to one side of the equation, leaving your target variable isolated. When doing this be careful that you follow reverse order of operations: Subtraction, Addition, Division, Multiplication, Exponents, Parentheses. Step 5. Solve for the target variable. You are done when target variable is isolated. Keep in mind that due to all the variables, you will not be able to simplify your equations as much as you are used to in linear algebra. When your target variable is isolated on one side of the equation, with all the other variables on the other side, you are done. Example 1: Application The formula C = d gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol in your answer. Locate d in the equation. Since d is multiplied by , divide both sides by to undo the multiplication. Now use this formula and the information given in the problem. Example 1: Application Continued The formula C = d gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol in your answer. Now use this formula and the information given in the problem. The bowl's diameter is I inches. Example 2: the distance formula Solve the formula d = rt for t. Find the time in hours that it would take Zach to travel 26.2 miles if his average speed was 18 miles per hour. d = rt Locate t in the equation. Since t is multiplied by r, divide both sides by r to undo the multiplication. Now use this formula and the information given in the problem. Example 2 continued… Solve the formula d = rt for t. Find the time in hours that it would take Zach to travel 26.2 miles if his average speed was 18 miles per hour. Zach’s time was about 1.46 hours. Example 3: Area of a Triangle Formula The formula for the area of a triangle is A = bh, where b is the length of the base, and is the height. Solve for h. A= bh 2A = bh Locate h in the equation. Since bh is multiplied by , divide both sides by to undo the multiplication. Since h is multiplied by b, divide both sides by b to undo the multiplication.