mm mm OFF ON ZERO Name Date Practice A For use with pages 390 395 Evaluate the expression for the given value of the variable.. 2 x 2 3 4; 25 2. 3 2x 8 2 0; 3 3. 24 x 2 9 ; 26 Match the equation with its solution. 4. x 2 3 5 5 5. x 3 5 5 6. x 5 5 6 A. x 52 and x 5 B. x 528 and x 5 2 C. x 5 8 and x 522 7. x 5 7 8. x 5 22 9. x 5.5 0. x 2 5 9. x 2 4 5 2. 2x 5 24 3. 3x 2 4 5 5 4. 4x 6 5 8 5. 2 x 5 5 8 Match the description with the appropriate equation. 6. The absolute deviation of x from 28 is 2. A. x 2 8 5 2 7. The absolute deviation of x from 8 is 2. B. x 2 2 5 8 8. The absolute deviation of x from 2 is 28. C. x 8 5 2 9. The absolute deviation of x from 2 is 8. D. x 2 2 528 Find the values of x that satisfy the definition of absolute value for the given value and the given absolute deviation. 20. Given value: 0; absolute deviation: 6 2. Given value: 3; absolute deviation: 4 22. Given value: 5; absolute deviation: 0 23. Given value: 2; absolute deviation: 4 24. Shampoo Prices The average price of the brand of shampoo that you buy is $4.50 for a bottle that holds 5 fluid ounces. Depending on where you shop, the prices vary by as much as $.5. a. Write an absolute value equation that represents the minimum and maximum prices of the shampoo. b. Find the minimum and maximum prices of the shampoo. 25. Calipers A caliper is a tool used for measuring objects as accurately as possible. The caliper shown below takes measurements with an absolute error of 0.02 millimeter. An object s width is measured using the caliper, which records a width of 4.5 millimeters. Find the minimum and maximum possible widths of the object. mm in 60
Practice B For use with pages 390 395. x 5 9 2. x 5 2.25 3. x 5 } 3 2 4. x 2 6 5 4 5. x 5 8 6. 2x 2 3 5 5 7. 4x 5 5 8. 7x 2 5 23 9. 5 2 2x 5 9 0. 3 2x 2 2 5 8. 4 5x 2 5 36 2. 2 6x 5 2 5 25 Solve the equation, if possible. 3. x 3 2 4 5 2 4. x 2 8 2 9 525 5. x 3 2.5 5 3 6. 26 0 2 2x 5 24 7. 23 4x 3 529 8. 24 5 2x 5 26 9. 2 } 3 2 8x 5 2 20. 3x 2 8 0.25 5 0.75 2. 6x 5 2.3 52.9 Find the values of x that satisfy the definition of absolute value for the given value and the given absolute deviation. 22. Given value: 3; absolute deviation: 5 23. Given value: ; absolute deviation: 7 24. Given value: 24; absolute deviation: 2 25. Given value: 22.5; absolute deviation: 8 26. Food Scale Bakers will typically weigh out flour for recipes rather than use a measuring cup because weighing is a more accurate measure. A baker is using a scale that has an absolute error of 0.05 gram. a. Find the minimum and maximum possible weights if the scale is used to measure out 225 grams of flour. b. Find the minimum and maximum possible weights if the scale is used to measure out 300 grams of flour. c. Find the minimum and maximum possible weights if the scale is used to measure out 420 grams of flour. 27. Toothpaste Prices The average price of the brand of toothpaste that you buy is $2.49 for an 8.2-ounce tube. Depending on where you shop, the prices vary by as much as $.5. a. Write an absolute value equation that represents the minimum and maximum prices of the toothpaste. b. Find the minimum and maximum prices of the toothpaste. c. You have a coupon for $.50 off two tubes of toothpaste. If you go to the store that has the minimum price for the toothpaste, how much will you pay for two tubes? 6
Practice C For use with pages 390 395. x 2 5 5 26 2. 0 2 x 5 9 3. 4x 5 7 4. 3x 2 4 5 8 5. 8 2 2x 5 22 6. 5 6x 2 3 5 30 7. } 4 2x 2 0 5 5 8. 8 2x 7 2 5 23 9. 25 3x 2 3 527 Solve the equation, if possible. 0. x 2 6 8 5 6. x 7 0 5 6 2. 24 2 7 } 2 x 528 3. 28 0 2 3x 5 24 4. 23 2 } 3 4 x 528 5. 22 5 2 x 2 3 529 6. 5 } 3 4x 4 5 24 7. 24 } 2 3 x 2 6 5 5 8. 28 3x 2 2 9 524 Find the values of x that satisfy the definition of absolute value for the given value and the given absolute deviation. 9. Given value: 2.5; absolute deviation: 4.5 20. Given value: 6.8; absolute deviation: 7.3 2. Given value: 28.; absolute deviation:.3 22. Given value: 29.4; absolute deviation: 2.2 23. How many solutions does the equation a x b c 5 d have if a < 0 and c 5 d? If a < 0, d > 0, and c < d? Explain. 24. Truck Scale If you travel along a highway, you will notice that there are weigh stations for large trucks. The purpose of these stations is to make sure that these trucks are traveling with loads that are not too heavy. A truck with a load that is too heavy can be unsafe and cause damage to the roads. The absolute error for a scale at a weigh station is 0% of the total weight. a. Find the maximum and minimum possible weights of a truck that is weighed with the scale and weighs 35,000 pounds. b. Find the maximum and minimum possible weights of a truck that is weighed with the scale and weighs 46,000 pounds. c. Find the maximum and minimum possible weights of a truck that is weighed with the scale and weighs 63,500 pounds. 25. Driving You have been keeping a record of how long it takes you to get home from work during good weather. The times range from 20 minutes to 45 minutes. Let t represent the slowest or fastest time (in seconds). Write an absolute value equation that describes the situation. 62
Challenge Practice For use with pages 390 395 In Exercises 5, solve the equation, if possible.. 2x 3 5 x 2. 3 2 2x 5 x 3. 2x 5 x 2 4. 2x 22x 5 2 5. x 5 5 x 5 In Exercises 6 0, use the following information to solve the equation, if possible. The expression x 2 a represents the distance between points x and a on the real number line. If you write x 2 a 5 b, then you are saying that x and a are b units apart on the real number line. So the values of x must be a 2 b or a b. For example: Solve x 2 2 5 5. x 5 2 2 5 or x 5 2 5 x 5 23 or x 5 7 6. x 2 4 5 7 7. x 6 5 2 8. x 2 3 5 5 and x 2 7 5 9 9. x 4 5 3 and x 2 5 2 0. x 2 5 5 0 and 2x 2 5 5 25 67
Problem Solving Workshop: Worked Out Example For use with pages 3902395 PROBLEM Manufacturing The diameter of a drill bit should be 0.5 inch with an absolute error of 0.005 inch. Find the minimum and maximum acceptable diameter of the drill bit. STEP Read and Understand What do you know? You know the diameter of the drill bit and the absolute error. What do you want to fi nd out? The minimum and maximum acceptable diameter of the drill bit. STEP 2 Make a Plan Use what you know to write and solve an absolute value equation. STEP 3 Solve the Problem Let d be the diameter (in inches) of the drill bit. Write a verbal model. Then write and solve an absolute value equation. Absolute deviation 5 Measured diameter 2 Accepted diameter 0.005 5 d 2 0.5 0.005 5 d 2 0.5 Write original equation. 66 PRACTICE 0.005 5 d 2 0.5 or 20.005 5 d 2 0.5 Rewrite as two equations. 0.505 5 d or 0.495 5 d Add 0.5 to each side. The minimum and maximum acceptable diameters are 0.495 inch and 0.505 inch. STEP 4 Look Back Substitute the minimum and maximum values in for d to see if the absolute deviation is 0.005. d 2 0.5 5 0.505 2 0.5 d 2 0.5 5 0.495 2 0.5 5 0.005 5 0.005 The answers are correct.. Boxing The middleweight division in boxing is centered at 64 pounds. A boxer s weight can have an absolute deviation of 4 pounds. Find the minimum and maximum acceptable weights for the middleweight division. 2. Car Mileage Your car averages 20 miles per gallon in the city. The actual mileage varies from the average by an absolute error of 4 miles per gallon. Find the minimum and maximum miles per gallon in the city. 3. Gymnastics A gymnast is preparing a floor program for a competition. The program must last 2 minutes with an absolute deviation of 5 seconds. Find the least and greatest possible times (in seconds) that the program can last. 4. Basketball Melissa s basketball scoring average is 8 points per game. Her highest and lowest points per game were both 2 points away from the average. Find Melissa s highest and lowest points per game.
Study Guide For use with pages 390 395 GOAL Solve absolute value equations. Vocabulary An absolute value equation, such as x 5 3, is an equation that contains an absolute value expression. The absolute deviation of a number x from a given value is the absolute value of the difference of x and the given value: absolute deviation 5 x 2 given value. EXAMPLE Solve an absolute value equation a. x 5 3 b. x 2 5 9 Solution a. The distance between x and 0 is 3. So, x 5 3 or x 523. The solutions are 3 and 2 3. b. Rewrite the absolute value equation as two equations. Then solve each equation separately. x 2 5 9 Write original equation. x 2 5 9 or x 2 529 Rewrite as two equations. x 5 7 or x 52 Subtract 2 from each side. The solutions are 7 and 2. Check your solutions. CHECK x 2 5 9 Write original inequality. 7 2 0 9 2 2 0 9 Substitute for x. Exercises for Example 9 0 9 29 0 9 Add. 9 5 9 9 5 9 Simplify. The solution checks.. x 5 0.4 2. x 2 4 5 3 3. 2x 2 5 7 63
Study Guide continued For use with pages 390 395 EXAMPLE 2 Rewrite an absolute value equation Solve } 2 3x 2 6 7 5 3. Solution First, rewrite the equation in the form ax b 5 c. } 2 3x 2 6 7 5 3 Write original equation. } 2 3x 2 6 5 6 Subtract 7 from each side. 3x 2 6 5 2 Multiply each side by two. Next, solve the absolute value equation. 3x 2 6 5 2 Write absolute value equation. 3x 2 6 5 2 or 3x 2 6 522 Rewrite as two equations. 3x 5 8 or 3x 526 Add 6 to each side. x 5 6 or x 522 Divide each side by 3. The solutions are 6 and 22. EXAMPLE 3 Decide if an equation has no solution Solve 2x 2 4 5 3, if possible. Solution 2x 2 4 5 3 Write original equation. 2x 2 52 Subtract 4 from each side. The absolute value of a number is never negative. So, there are no solutions. Exercises for Examples 2 and 3 Solve the equation, if possible. 4. 2 x 2 2 5 5 9 5. 5 x 2 4 5 8 6. } 5 2x 2 3 2 4 5 64