EXAMPLE 1 Solve a simple absolute value equation Solve |x – 5| = 7. Graph the solution. SOLUTION | x – 5 | = 7 x – 5 = – 7 or x – 5 = 7 x = 5 – 7 or x

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<ul><li>Slide 1</li></ul> <p>EXAMPLE 1 Solve a simple absolute value equation Solve |x 5| = 7. Graph the solution. SOLUTION | x 5 | = 7 x 5 = 7 or x 5 = 7 x = 5 7 or x = 5 + 7 x = 2 or x = 12 Write original equation. Write equivalent equations. Solve for x. Simplify. Slide 2 EXAMPLE 1 The solutions are 2 and 12. These are the values of x that are 7 units away from 5 on a number line. The graph is shown below. ANSWER Solve a simple absolute value equation Slide 3 EXAMPLE 2 Solve an absolute value equation | 5x 10 | = 45 5x 10 = 45 or 5x 10 = 45 5x = 55 or 5x = 35 x = 11 or x = 7 Write original equation. Expression can equal 45 or 45. Add 10 to each side. Divide each side by 5. Solve |5x 10 | = 45. SOLUTION Slide 4 EXAMPLE 2 Solve an absolute value equation The solutions are 11 and 7. Check these in the original equation. ANSWER Check: | 5x 10 | = 45 | 5(11) 10 | = 45 ? |45| = 45 ? 45 = 45 | 5x 10 | = 45 | 5(7) 10 | = 45 ? 45 = 45 | 45| = 45 ? Slide 5 EXAMPLE 3 | 2x + 12 | = 4x 2x + 12 = 4x or 2x + 12 = 4x 12 = 2x or 12 = 6x 6 = x or 2 = x Write original equation. Expression can equal 4x or 4 x Add 2x to each side. Solve |2x + 12 | = 4x. Check for extraneous solutions. SOLUTION Solve for x. Check for extraneous solutions Slide 6 EXAMPLE 3 | 2x + 12 | = 4x | 2(2) +12 | = 4(2) ? |8| = 8 ? 8 = 8 Check the apparent solutions to see if either is extraneous. Check for extraneous solutions | 2x + 12 | = 4x | 2(6) +12 | = 4(6) ? |24| = 24 ? 24 = 24 The solution is 6. Reject 2 because it is an extraneous solution. ANSWER CHECK Slide 7 GUIDED PRACTICE Solve the equation. Check for extraneous solutions. 1. | x | = 5 for Examples 1, 2 and 3 The solutions are 5 and 5. These are the values of x that are 5 units away from 0 on a number line. The graph is shown below. ANSWER 3 4 2 1 0 1 234 5 6 7 5 6 7 5 5 Slide 8 GUIDED PRACTICE Solve the equation. Check for extraneous solutions. 2. |x 3| = 10 for Examples 1, 2 and 3 The solutions are 7 and 13. These are the values of x that are 10 units away from 3 on a number line. The graph is shown below. ANSWER 3 4 2 1 0 12345 6 7 5 6 78 9 10 11 12 13 10 Slide 9 GUIDED PRACTICE Solve the equation. Check for extraneous solutions. 3. |x + 2| = 7 for Examples 1, 2 and 3 The solutions are 9 and 5. These are the values of x that are 7 units away from 2 on a number line. ANSWER Slide 10 GUIDED PRACTICE Solve the equation. Check for extraneous solutions. 4. |3x 2| = 13 for Examples 1, 2 and 3 ANSWER The solutions are 5 and. Slide 11 GUIDED PRACTICE Solve the equation. Check for extraneous solutions. 5. |2x + 5| = 3x for Examples 1, 2 and 3 The solution of is 5. Reject 1 because it is an extraneous solution. ANSWER Slide 12 GUIDED PRACTICE Solve the equation. Check for extraneous solutions. 6. |4x 1| = 2x + 9 for Examples 1, 2 and 3 ANSWER The solutions are and 5. 3 1 1 </p>

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