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Solving Absolute Value Equations and Word Problems Name May 12, 2011 1. Review of Solving Absolute Value Equations Example: | x – 2 | = 10 Remember to drop the absolute value sign and set the left side of the equation equal to both 10 and -10 Then, solve for x in both equations x – 2 = 10x – 2 = -10 | x – 2 | = 10 OR +2 = +2 x = 12 +2 = +2 x = -8 OR

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Solving Absolute Value Equations and Word Problems Name May 12, 2011 2. Absolute Value Equations WITH TERMS OUTSIDE ABSOLUTE VALUE SIGNS Sometimes there are terms outside of the absolute value sign First, isolate the terms in the absolute value sign | x – 3 | + 4 = 8 x – 3 = 4x – 3 = -4 | x – 3 | = 4 Second, remove absolute value signs and solve two equations OR -4 = -4

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Solving Absolute Value Equations and Word Problems Name May 12, 2011 3. Examples x + 3 = 15x + 3 = -15 Ex 2:| x + 3| – 5 = 10 OR -3 = -3 x = 12 -3 = -3 x = -18 OR | 12 + 3 | – 5 = 10 CHECK: | x + 3 | = 15 +5 = +5 | -18 + 3 | – 5 = 10 | 15 | – 5 = 10 | -15 | – 5 = 10 15 – 5 = 10

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Solving Absolute Value Equations and Word Problems Name May 12, 2011 3. Examples x + 5 = 18x + 5 = -18 Ex 3:| x + 5| + 7 = 25 OR -5 = -5 x = 13 -5 = -5 x = -23 OR | 13 + 5 | + 7 = 25 CHECK: | x + 5 | = 18 -7 = -7 | -23 + 5 | + 7 = 25 | 18 | + 7 = 25 | -18 | + 7 = 25 18 + 7 = 25

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Solving Absolute Value Equations and Word Problems Name May 12, 2011 4. Absolute Value Word Problems The temperature at 6am was 37ºF. The temperature at 2pm was 65ºF. The temperature at 10pm was 33ºF. Using absolute value, determine if the temperature change in the morning was more than the change at night. What are we trying to find? What do we know? If the temperature change in morning was more than the change at night Temp in ºF 6am: 37, 2pm: 65, 10pm: 33 Use Absolute value Chg in morn and night IT SAYSI SAY Morning is chg from 6am to 2pm Night is chg from 2pm to 10pm Abs must be positive

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Solving Absolute Value Equations and Word Problems Name May 12, 2011 4. Absolute Value Word Problems The temperature at 6am was 37ºF. The temperature at 2pm was 65ºF. The temperature at 10pm was 33ºF. Using absolute value, determine if the temperature change in the morning was more than the change at night. How do we solve it? Did we answer the original question? Change in Morning: | 65 – 37 | = |28| = 28ºF Change at Night: | 33 – 65 | = |-32| = 32ºF Chg at Morn < Chg at Night 28ºF < 32ºF YES! The answer is no. The change at night was more than the change during the morning by 4ºF.

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Solving Absolute Value Equations and Word Problems Name May 12, 2011 4. Absolute Value Word Problems Uplift is on Wilson Ave, which is 4600 North (in grid coordinates). Brianna lives at 2000 North and Chris lives at 7000 North. Assume everyone lives on Sheridan/Sheffield. Using absolute value, determine who lives further from Uplift. What are we trying to find? What do we know? Who lives further from Uplift (in grid coordinates) Uplift 4600 North Brianna 2000 North Chris 7000 North Use Abs Value IT SAYSI SAY Chicago map, in line north to south Grid coordinates measure blocks in Chicago Abs value is always positive 7000N 2000N 4600N

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Solving Absolute Value Equations and Word Problems Name May 12, 2011 4. Absolute Value Word Problems How do we solve it? Did we answer the original question? Brianna Distance from Uplift: |2000 – 4600| = |-2600| = 2600 Chris Distance from Uplift |7000 - 4600| = |2400| = 2400 Brianna Dist. > Chris Dist. 2600 > 2400 YES! Brianna lives further from Uplift than Chris by 200 Uplift is on Wilson Ave, which is 4600 North (in grid coordinates). Brianna lives at 2000 North and Chris lives at 7000 North. Assume everyone lives on Sheridan/Sheffield. Using absolute value, determine who lives further from Uplift. 7000N 2000N 4600N 2400 2600

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The absolute value of a number is its distance from 0. Absolute value is always positive. For example, from here to D.C. is approximately 40 miles.

The absolute value of a number is its distance from 0. Absolute value is always positive. For example, from here to D.C. is approximately 40 miles.

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