Section 2.6 Formulas and Applications of Geometry 147 a 5 ft c ? b 7 ft If the perimeter is 20 ft, then c P a b 20 ft 5 ft 7 ft 8 ft Figure 2-8 To solve a formula for a different variable, we use the same properties of equality outlined in the earlier sections of this chapter. For example, consider the two equations 2x 3 11 and wx y z. Suppose we want to solve for x in each case: 2x 3 11 wx y z 2x 3 3 11 3 wx y y z y Subtract 3. Subtract y. 2x 8 wx z y wx w z y w Divide by 2. Divide by w. x z y w 2x 2 8 2 x 4 The equation on the left has only one variable and we are able to simplify the equation to find a numerical value for x.The equation on the right has multiple variables. Because we do not know the values of w, y, and z, we are not able to simplify further.The value of x is left as a formula in terms of w, y, and z. Solving for an Indicated Variable Example 1 Solve for the indicated variable. a. d rt for t b. 5x 2y 12 for y Solution: a. for t The goal is to isolate the variable t. Because the relationship between r and t is multiplication, we reverse the process by dividing both sides by r. or equivalently d rt b. for y The goal is to solve for y. Subtract 5x from both sides to isolate the y-term. 5x 12 is the same as 12 5x. Divide both sides by 2 to isolate y. 5x 5x 2y 12 5x 2y 5x 12 y 5x 12 2 2y 2 5x 12 2 5x 2y 12 t d r d r t, d r rt r
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