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2-5 ABSOLUTE VALUE EQUATIONS Goals: • Evaluate absolute value expressions • Solve absolute value equations. Eligible Content: A1.1.1.3.1 / A1.1.2.1.1 / A1.1.2.1.2 / A1.1.2.1.3 VOCABULARY Absolute Value – the distance from 0. EVALUATE EACH EXPRESSION 1. 2. 3. 4. 5. 6. 7. −17 39 5−8 − 28 − −12 𝑚 + 6 − 14 when m = 4 15 − 𝑥 + 7 when x = – 3 LOOK AT |X|= 5 What numbers can x be? x can be 5 or x can be -5 So x = 5 or x = -5 Check it! |5| = 5 AND |-5|= 5 Every absolute value problem has 2 answers! You must do 2 problems to find the 2 answers!!! SOLVE: 𝑥 − 2 = 5 The expression (x – 2) can be equal to 5 or –5!!! x – 2 is positive x – 2 is negative x–2=5 +2 +2 x=7 x – 2 = –5 +2 +2 x = –3 So x = 7 or x = –3 EXAMPLES 1. |x – 4|= 9 x = 13 or x = -5 2. |2x + 2|= 8 x = 3 or x = -5 3. |–4x – 7|= 12 x = -4.75 or x = 1.25 4. |p + 6| = –5 no solution Solve |2x + 3| = 5. Graph the solution set. A. {1, –4} B. {1, 4} C. {–1, –4} D. {–1, 4} Solve |x – 3| = –5. A. {8, –2} B. {–8, 2} C. {8, 2} D. PRACTICE Page 105 #1-9 WRITE AN ABSOLUTE VALUE EQUATION Find the midpoint between two points Find the distance to the midpoint from each point. Write equation: 𝑥 − midpoint = distance from midpoint to points EXAMPLES Write an equation for each graph. 1. 𝑥−1 =3 2. 𝑥−2 =6 3. 𝑥+5 =2 Write an equation involving the absolute value for the graph. A. |x – 2| = 4 B. |x + 2| = 4 C. |x – 4| = 2 D. |x + 4| = 2 WORD PROBLEM #1 The temperature of a snake enclosure should be about 80°F, give or take 5°. Use an absolute value equation to find the minimum and maximum temperature. 𝑥 − 80 = 5 x = 75 or x = 85 Minimum: 75° Maximum: 85° WORD PROBLEM #2 The average January temperature in a northern Canadian city is 1°F. The actual temperature may be about 7° warmer or colder. Use an absolute value equation to find the minimum and maximum temperature. 𝑥−1 =7 x = –6 or x = 8 Minimum: –6° Maximum: 8° WEATHER The average temperature for Columbus on Tuesday was 45ºF. The actual temperature for anytime during the day may have actually varied from the average temperature by 15ºF. Solve to find the maximum and minimum temperatures. A. {–60, 60} B. {0, 60} C. {–45, 45} D. {30, 60} HOMEWORK Page 106 #14-30 even #33-36