2 5 Solving for a Variable Objectives Solve

2 -5 Solving for a Variable Objectives Solve a formula for a given variable. Solve an equation in two or more variables for one of the variables. Holt Algebra 1

2 -5 Solving for a Variable A formula is an equation that states a rule for a relationship among quantities. In the formula A = ½bh, it is solved for A. That is useful only if you are told the base and height to plug in. What if you know that Area and the base, and you are trying to find the height? You can "rearrange" a formula to isolate any variable, like h, by using inverse (opposite) operations. This is called solving for a variable. Holt Algebra 1

2 -5 Solving for a Variable Step 1 Locate the variable you are asked to solve for in the equation. Step 2 Identify the operations on this variable and the order in which they are applied. Step 3 Use inverse operations to undo operations and isolate the variable. Holt Algebra 1

2 -5 Solving for a Variable Example 3: Solving Literal Equations A. Solve x + y = 15 for x. x + y = 15 –y –y x = –y + 15 B. Solve pq = x for q. pq = x Holt Algebra 1 Locate x in the equation. Since y is added to x, subtract y from both sides to undo the addition. Locate q in the equation. Since q is multiplied by p, divide both sides by p to undo the multiplication.

2 -5 Solving for a Variable Check It Out! Example 3 a Solve 5 – b = 2 t for t. 5 – b = 2 t Locate t in the equation. Since t is multiplied by 2, divide both sides by 2 to undo the multiplication. Holt Algebra 1

2 -5 Solving for a Variable Example 1: Application The formula C = d gives the circumference of a circle C in terms of diameter d. 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. Holt Algebra 1

2 -5 Solving for a Variable Example 2 A: Solving Formulas for a Variable 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 2 A = 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. Holt Algebra 1

2 -5 Solving for a Variable Check It Out! Example 2 The formula for an object’s final velocity is f = i – gt, where i is the object’s initial velocity, g is acceleration due to gravity, and t is time. Solve for i. f = i – gt +gt f + gt = i Holt Algebra 1 Locate i in the equation. Since gt is subtracted from i, add gt to both sides to undo the subtraction.

2 -5 Solving for a Variable Example 2 B: Solving Formulas for a Variable The formula for a person’s typing speed is , where s is speed in words per minute, w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for e. Locate e in the equation. Since w– 10 e is divided by m, multiply both sides by m to undo the division. Last divide both ms = w – 10 e Since w is added to sides by -10. –w –w 10 e, subtract w from ms – w = e ms – w = – 10 e both sides 1 -10 Holt Algebra 1

2 -5 Solving for a Variable Check It Out! Example 3 b Solve for V Locate V in the equation. VD = m Since m is divided by V, multiply both sides by V to undo the division. Since V is multiplied by D, divide both sides by D to undo the multiplication. Holt Algebra 1

2 -5 Solving for a Variable Partner Questions Solve for the indicated variable. 1. for h 2. P = R – C for C C=R–P 3. 2 x + 7 y = 14 for y 4. Holt Algebra 1 for m m = x(k – 6 )