SECTION 1.4 Solving Equations Using a Graphing Utility 31 SUMMARY Steps for Approximating Solutions of Equations Using ZERO (or ROOT) Step 1 Write the equation in the form { } = expression in x 0. Step 2 Graph { } = Y expression in x . 1 Be sure that the graph is complete. That is, be sure that all the x -intercepts are shown on the screen. Step 3 Use ZERO (or ROOT) or click on the graph to determine each x -intercept of the graph. Steps for Approximating Solutions of Equations Using INTERSECT Step 1 Graph { } { } = = Y expression in x on the left side of the equation Y expression in x on the right side of the equation 1 2 Be sure that the graphs are complete. That is, be sure that all the points of intersection are shown on the screen. Step 2 Use INTERSECT or click on the graph to determine the x -coordinate of each point of intersection. Solving a Linear Equation Solve the equation: ( ) ( ) − = − x x 3 2 5 1 EXAMPLE 3 Figure 46 ( ) = − Y x 3 2 ; 1 ( ) = − Y x 5 1 2 5 215 25 5 Y1 Y2 Algebraic Solution ( ) ( ) − = − − = − − − = − − − − = − − − + = − + − = − − = − = − x x x x x x x x x x x x x 3 2 5 1 3 6 5 5 3 6 5 5 5 5 2 6 5 2 6 6 5 6 2 1 2 2 1 2 1 2 Graphing Solution Graph ( ) = − Y x 3 2 1 and ( ) = − Y x 5 1 . 2 See Figure 46. Using INTERSECT, the point of intersection is found to be ( ) − − 0.5, 7.5 . The solution of the equation is −0.5. Use the Distributive Property. Subtract x5 from both sides. Simplify. Add 6 to both sides. Simplify. Divide both sides by −2. Simplify. Check: Substitute − 1 2 for x in the expressions on the left and right sides of the original equation, and simplify. If the two expressions are equal, the solution checks. ( ) ( ) ( ) ( ) ( ) ( ) − = − − = − = − − = − − = − = − x x 3 2 3 1 2 2 3 5 2 15 2 5 1 5 1 2 1 5 3 2 15 2 Since the two expressions are equal, the solution − 1 2 checks. The solution set is { } − 1 2 . Now Work PROBLEM 19 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 1.4 Assess Your Understanding 1. Solve the equation + + = x x 2 5 2 0. 2 (pp. A47–A53) 2. Solve the equation ( ) + = − + x x 2 3 4 1 1. (pp. A45–A47)
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