Practice A. Name Date. (8x 2 6) 5 1; 1. (m 2 4) 5 5. (w 2 7) 5 5. (d 2 5) (m 1 6) Total amount in piggy bank.

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1 Practice A For use with pages Check whether the given number is a solution of the equation.. 6x 2 5x 5 7; (m 2 4) 5 3; 3. } 2 (8x 2 6) 5 ; State the first step in solving the equation. 4. 3y 7y (a 2 4) } 3 (m 2 4) (w 2 3) d d ( p 6) 5 27 Solve the equation. 0. 3a 2a n 2 4 n c 3 2 5c y 4y (x ) (m 2 2) p 3(p 3) w 5(w 2 2) (x 2) (d 2 5) } 3 (m 6) } 8 (w 2 7) 5 5 Find the value of x for the triangle or rectangle. 22. Perimeter 5 7 feet 23. Perimeter 5 8 meters x ft 2x ft 5 ft 2x m 24. Target Heart Rate The target heart rate is the heartbeat rate during aerobic exercise that provides a benefit to your heart. The target heart rate for a person exercising at 70% intensity is given by the equation y 5 0.7(200 2 x) where y is the target heart rate in beats per minute and x is the person s age in years. a. How old is a person with a target heart rate of 33 beats per minute? b. How old is a person with a target heart rate of 26 beats per minute? 25. Spare Change You have quarters and nickels saved in a piggy bank. There is a total of $3.45 in quarters and nickels and there are 9 more nickels than quarters. a. Use the verbal model to write an equation that you can use to find the number of nickels and quarters in your piggy bank. Let q represent the number of quarters. Number of quarters p Value of quarter Number of nickels b. How many nickels and quarters are in the piggy bank? p Value of nickel x m 5 Total amount in piggy bank 29

2 Practice B For use with pages Solve the equation.. 6x x m 4 2 9m b b p 2 7p (x ) (d 2 5) a 5(a 2 3) a 2 3(a 2 6) (x 2 8) } 3 (d 9) (n 3) } 2 (w 2 ) (z 2 2) (6m 2) n 2 2.(n 2 4) Find the value of x for the triangle or rectangle. 6. Perimeter 5 23 feet 7. Perimeter 5 24 meters x ft (x + 3) ft (x + 3) m 2x ft 2x m 8. Wrapping a Package It takes 70 inches of ribbon to make a bow and wrap the ribbon around a box. The bow takes 32 inches of ribbon. The width of the box is 4 inches. What is the height of the box? 4 in. x 9. Vacation You are driving to a vacation spot that is 500 miles away. Including rest stops, it takes you 42 hours to get to the vacation spot. You estimate that you drove at an average speed of 50 miles per hour. How many hours were you not driving? 20. Moving You helped a friend move a short distance recently. The friend rented a truck for $5 an hour and rented a dolly for $5. Your friend paid a total of $80 for the rental. For how long did your friend rent the truck? 2. Painting You and your friend are painting the walls in your apartment. You estimate that there is 000 square feet of space to be painted. You paint at a rate of 4 square feet per minute and your friend paints at a rate of 3 square feet per minute. Your friend shows up to help you paint 45 minutes after you have already started painting. a. Write an equation that gives the total number of square feet y as a function of the number of minutes x it takes to paint all of the walls. b. How long will it take you and your friend to finish painting? Round your answer to the nearest minute. 30

3 Practice C For use with pages Solve the equation.. 23x x m 2 33m b b p 2 3p (x 4) (2d 2 ) a 2 4(5a 2) a 2 4(3a 7) (x 2 5) } 5 (5m 5) } 8 (2p 2 ) } 3 (3w 2 2) (z 2 4) (4m 3) n 2 (2n 2 5) Find the value of x for the triangle or rectangle. 6. Perimeter 5 32 feet 7. Perimeter 5 24 meters x ft (x + 7) ft (x + ) m 3x ft (3x + ) m 8. Class Reunion You are traveling 80 miles back to your home town for a class reunion. About 60 miles of the trip are through areas where the speed limit is 45 miles per hour and the rest of the trip is through areas where the speed limit is 55 miles per hour. Assuming that you can travel at the speed limits to get to the reunion, how long will it take you? Round your answer to the nearest tenth. 9. Retaining Wall You and two friends are building a retaining wall. The estimate for the number of blocks in the wall is 500 blocks. You and one of your friends have experience building retaining walls, so you each can install 20 blocks per hour. Your other friend, who is doing this for the first time, can install about 8 blocks per hour. You had a dentist appointment and showed up hour after your friends started on the wall. How long will it take you to build the wall? Round your answer to the nearest hour. How many blocks will each of you install? 20. Installing Shelves You are hanging 3 display shelves with the same width on a wall so that there is 8 inches of space above each shelf for placing items. Each shelf is 3 inches wide. You want the space from the ceiling to the top 8 inches of space and the space below the bottom shelf to a chair rail to be the same. Determine the distance from the ceiling to the bottom of each of the shelves so that you can install them. Explain how you got your answer. 8 in. 8 in. 8 in. 7 in. 3

4 Challenge Practice For use with pages In Exercises 6, use n to represent an integer, 2n to represent an even integer, and 2n to represent an odd integer.. Find three consecutive integers whose sum is Find three consecutive even integers whose sum is Find three consecutive odd integers whose sum is Find four consecutive integers whose sum is Find four consecutive even integers whose sum is Find four consecutive odd integers whose sum is Manuel has pennies and nickels with a total value of $.5. The number of nickels is 43 less than the number of pennies. How many pennies does Manuel have? 8. Alicia has five times as many dimes as she has quarters. Combined the dimes and quarters total to $9.75. How many dimes does Alicia have? 9. Lola has twice as many quarters and half as many nickels as does Ellen. Ellen has $6.30 in quarters and nickels and has 6 less nickels than quarters. How much money does Lola have? 36

5 Problem Solving Workshop: Using Alternative Methods For use with pages Another Way to Solve Example 5 on page 50 Multiple Representations In Example 5 of page 50, you saw how to solve a problem about bird migration using a verbal model. You can also solve the problem by solving a simpler problem. PROBLEM METHOD Bird Migration A flock of cranes migrates from Canada to Texas. The cranes take 4 days (336 hours) to travel 2500 miles. The cranes fly at an average speed of 25 miles per hour. How many hours of the migration are the cranes not flying? Solving a Simpler Problem You can solve the problem by solving a simpler problem. STEP Write an equation for the amount of time the cranes are flying. Let h be the amount of time the cranes are flying. Distance (miles) 5 Rate (miles/hour) p Time spent flying (hours) p h An equation for the amount of time the cranes are flying is h. STEP 2 Find the amount of time the cranes are flying h Write equation h Divide each side by 25. The cranes were flying for 00 hours of the migration. PRACTICE STEP 3 Find the amount of time the cranes were not flying by subtracting the length of time of the migration by the amount of time flying The cranes were not flying for 236 hours of the migration.. Swimming Amanda swims at an average rate of 72 meters per minute. It takes her 36 minutes to finish 800 meters with breaks. How many minutes did Amanda swim? How many minutes of breaks did she take? Solve this problem using two different methods. 2. What If? Suppose in Example that Amanda wants to swim 2700 meters and finish in 45 minutes. How many minutes of breaks did she take? 3. Jogging Mark works out for 50 minutes by biking and jogging. He bikes at an average rate of 200 feet per minute and jogs at an average rate of 900 feet per minute. He wants to travel a combined 0 miles ( mile feet). How many minutes did Mark spend jogging? 4. Perimeter The sides of a triangle have lengths (3x ) feet, (2x 2 3) feet, and x feet. The perimeter of the triangle is 22 feet. Find the value of x. 35

6 Graphing Calculator Activity: Solving a Linear Equation For use before Lesson QUESTION How can you use a graphing calculator to solve a linear equation graphically? You can solve a linear equation by graphing each side of the equation. The x-value where the graphs intersect is the solution of the equation. EXAMPLE Solve a linear equation graphically Use a graphing calculator to solve 2 x 5 7 graphically. STEP Enter each side of the equation. Press Y=. Enter the left side of the equation as y Plot Plot2 Plot3 and the right side of the equation as y 2. \Y=2+X \Y2=7 \Y3= \Y4= \Y5= \Y6= \Y7= PRACTICE STEP 2 Set window. The screen is a window that lets you look at part of a graph. Press WINDOW. A friendly window for y and y 2 is 20 x 0 and 20 y 0. Note that you can also obtain this window by pressing ZOOM 6. STEP 3 Graph and solve. Press 2nd [CALC] 5 to graph y and y 2 and to find the point of intersection. The x-value of the point of intersection is the solution of the linear equation. From the graph, you can see that the x-value is 25. Check this answer in the original equation. WINDOW Xmin=-0 Xmax=0 Xscl= Ymin=-0 Ymax=0 Yscl= Xres=_ Intersection X=-5 Y=7 Solve the equation graphically. Use the window given in the example.. x x x 2 2 x x x 5. 5(2x 2 7) 2 3x (x 3) 7. 24x 3(x 2 ) x 2(4 2 3x) 9..2(3 2 x)

7 Graphing Calculator Activity: Solving a Linear Equation continued For use before Lesson TI-83 Plus Y= 2 X,T,,n ENTER 7 ENTER ZOOM 6 2nd [CALC] 5 Casio CFX-9850GC Plus From the main menu, choose GRAPH. 2 X,,T EXE 7 EXE SHIFT F3 F3 EXIT F6 SHIFT F5 F5 28

8 Study Guide For use with pages GOAL Solve multi-step equations. EXAMPLE Solve an equation by combining like terms Solve 7x 2 x Solution 7x 2 x x x x 5 2 Write original equation. Combine like terms. Subtract 8 from each side. Simplify. 6x } } 6 Divide each side by 6. x 5 2 Simplify. Exercises for Example Solve the equation. Check your solution.. 9x 2 3x x 8x 522 EXAMPLE x x x 2 4x 5224 Solve an equation using the distributive property Solve 4x 3(2x 2 ) 5 7. Solution METHOD Show All Steps METHOD 2 Do Some Steps Mentally 4x 3(2x 2 ) 5 7 4x 3(2x 2 ) 5 7 4x 6x x 6x x x x x x 5 20 x 5 2 0x } 0 5 } 20 0 x

9 Study Guide continued For use with pages Exercises for Example 2 Solve the equation. Check your solution. 5. 3(x 2 4) 4x x 2 6(3x 2 3) x 7(3x 2) (2x 8) 2 6x 5 6 EXAMPLE 3 Multiply by a reciprocal to solve an equation Solve 3 (5x 2 4) 5 2. Solution 3 (5x 2 4) 5 2 Write original equation. 4 } 3 p 3 (5x 2 4) 5 4 } 3 p 2 Multiply each side by 4 } 3, the reciprocal of 3. 5x x 5 20 x 5 4 Simplify. Subtract 4 from each side. Simplify. Exercises for Example 3 Solve the equation. Check your solution. 9. } 2 (x 2 ) } 2 (2y 6) } 7 (4z 2 ) (5m 2) 33