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Published byJeanette Gilman Modified over 2 years ago

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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 = x = –2 or x = 12 Write original equation. Write equivalent equations. Solve for x. Simplify.

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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

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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

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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 ?

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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

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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

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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 – – 5 – 6 – 7 5 5

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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 – – 5 – 6 –

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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

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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.

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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

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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

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