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Solving Absolute Value Equations • The absolute value of x is defined as x, if x 0 x x, if x 0 • Example 1 8 8 8 Table of Contents x, if x 0 x x, if x 0 • Example 2 7 7 Table of Contents • Example 3 x 4 Solve: Since 4 4 the solution is and 4 4 x 4, 4 or x 4 The process used above leads to our method for solving absolute value equations. Table of Contents • To solve the absolute value equation expression b 1) Write expression b expression b 2) Solve the resulting equations. Table of Contents • Example 4 Solve: 2 x 7 3 2 First, add 3 to both sides to get the equation in the form of expression b 2x 7 1 Table of Contents 2x 7 1 Write the two equations and solve each. 2x 7 1 2x 7 1 2x 6 2x 8 x3 x4 x 3, 4 Table of Contents • Example 5 Now solve the same problem again, only this time use the graphing method. 2 x 7 3 2 Move all terms to the left hand side. 2x 7 3 2 0 y1 Let y1 equal the left hand side. Table of Contents 2x 7 3 2 0 Enter the expression for y1 into the calculator Press Zoom-6 to graph Use Trace to find the x-intercepts Table of Contents y1 Press Trace and then enter 3. Since the y-value is 0, (3,0) is an x-intercept, and 3 is a solution to the equation. Now repeat the process with x = 4, the intercept on the right. Again, the y-value is 0. The solutions to the equation are x = 3,4 Table of Contents Table of Contents