1. Algebra 1 Unit 2. 1. Students will be able to solve two-step equations. (Section
... + 1 = 8. 7. 5x + 8 = 0. 8. –8 + x. 4. = 12. 9. x. 5. 6. = –7. 10. 1. 2 x + 3 = 9. 11.
Algebra 1 Unit 2 1.
Students will be able to solve two-step equations. (Section 2.1) Worksheet 1 1 - 24 Page 72 1 – 54 (optional)
2.
Students will be able to solve word problems by substituting data into a given equation. Worksheet 2 1 – 12
3.
Students will be able to solve multi-step equations that involve the distributive property and/or combining like terms on each side of the equation. (Section 2.2) Worksheet 3 1 - 22 Page 79 13 – 52 (optional)
4.
Students will be able to solve equations with variables on both sides of the equation. (Section 2.3) Page 86 1 – 14, 18 - 31
5.
Students will be able to translate sentences to algebraic equations and then solve. Worksheet 5 1 - 10
6.
Students will be able to solve word problems about consecutive integers and perimeter. (Section 2.5) Page 104 1–7 Worksheet 6 1-8
7.
Students will be able to solve word problems that involve comparisons involving 2 or more items. Worksheet 7 1–7
Review Worksheet 1 Review Worksheet 2
Algebra 1 Unit 2
1 – 30 1 - 19
1
Unit 2 Worksheet 1 Solve: 1.
2x + 1 = 9
2.
3x + 4 = – 11
3.
4.
7x – 2 = 19
5.
7.
5x + 8 = 0
8.
10.
1 x+3=9 2
11.
3x + 42 = 0
12.
9x – 7 = 0
13.
3 – 2x = 17
14.
12 = 6 – 3x
15.
–3x – 4 = 1
x + 1 = 15 2 x –8 + = 12 4
4x – 5 = –9 x + 1 = 8 7 x 5 = –7 6
6. 9.
In problems 16 – 24, select the correct multiple choice answer. 16.
17.
Which equation is equivalent to A.
3x = - 24
B.
3x = - 6
C.
3x = - 14
D.
3x = - 10
?
Which equation is equivalent to –5x + 1 = –17 ? A. 5x = 18 B. 5x = –18 C.
18.
3x – 2 = - 12
5x = –16
D.
5x = 16
Max is solving the equation 3x – 2 = 10 Which of the following are correct steps to find the solution? A. B. C.
19.
Divide both sides by 3. Then add 2 to both sides. Add 2 to both sides. Then divide both sides by 3. Subtract 2 from both sides. Then divide both sides by 3. 1 D. Multiply both sides by . Then subtract 2 from both sides. 3 Which of the following are correct steps to find the solution of the following equation? 8 = 18 – 2x A. Subtract 18 from both sides and divide by 2. B. Subtract 8 from both sides and divide by 2 C. Subtract 18 from both sides and divide by – 2 D. Subtract 8 from both sides and divide by – 2.
Algebra 1 Unit 2
2
20.
Four students worked the following equation. Their work is shown below. x Identify which one student did the work correctly. + 4 = 7 3 Alice x + 4 = 7 3
21.
22.
23.
24.
Bill x + 4 = 7 3
Chu x + 4 = 7 3
x 3
= 11
x 3
=
3
x 3
=
x
=
x
=
1
x
= 9
33
3
Danielle x + 4 = 7 3 x + 4 = 21 x
= 17
Which of the following are correct steps to find the solution of the following x equation? 5 + = 9 2 A. Multiply both sides by 2 and subtract 5. B.
Multiply both sides by -2 and subtract 5.
C.
Subtract 5 from both sides and multiply by 2
D.
Subtract 5 from both sides and divide by 2.
What is the multiplicative inverse of A.
–
C.
7 8
8 7
–
B.
8 7
D.
1
7 ? 8
What is the value of x in the equation 6x + 5 = 0 ? A.
5 6
C.
–
6 5
B.
6 5
D.
–
5 6
Which equation is equivalent to 5 – 2x = 12 ? A.
2x = 7
B.
2x = –7
C.
2x = 17
D.
2x = –17
Algebra 1 Unit 2
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Unit 2 Worksheet 2 1.
The total number of cups of flour (f) that McKenna has left after baking (c) number of cakes is given by the equation f = –9c + 80 a) If McKenna bakes 3 cakes how much flour will she have left? b)
2.
The amount of time (t) in seconds it takes a cashier to ring up a customer is related to (n) the number of items they purchase. The equation is t = n + 12 a) How long does it take to ring up a customer with 5 items? b)
3.
If it took 30 seconds to ring up a customer, how many items did they purchase?
The number of pictures (p) that Lola takes depends on the number of days (d) she is on vacation. The equation is p = 5d + 2 a) If Lola took 37 pictures, how many days was she on vacation? b)
4.
If McKenna has 17 cups of flour how many cakes did she bake?
If Lola vacations for 10 days, how many pictures will she take?
The equation below is used to show the number of napkins that Ken has left is related to the number of tables that he has set. n = –8t + 200 a) If Ken has 120 napkins left, how many tables did he set? b)
If Ken sets 25 tables, how many napkins will he have left?
5.
The distance (d) in miles that Cecil runs depends on the number of track practices (p) he attends. d = 2p + 3 How many miles would Cecil run if he attended 5 practices?
6.
The amount of fabric (f) in yards used to sew n number of shirts can be found 3 using the equation f = n 4 If 12 yards of fabric were used, how many shirts were sewn?
Algebra 1 Unit 2
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7.
The number of fish (f) Bill catches is related to the number of days (d) he goes fishing. f = 2d + 2 If Bill fishes for 8 days, how many fish will he catch?
8.
The height of a plant in inches (i) is related to the number of days (d) you care 1 for and water the plant. i= d+2 2 If a plant is 10 inches tall how many days was it cared for?
9.
When digging into the earth, the temperature (t) in Celsius rises according to the 1 depth (d) in meters. t = 15 + d 100 a) What will the temperature be at 100 meter? b)
10.
A faucet drips (d) ounces of water every m minutes as shown in the equation 2 d = m + 10 5 a) How many ounces of water will it have dripped after 20 minutes? b)
11.
At what depth would the temperature be 24° C ?
How long will it take for it to drip 30 ounces?
Many times the actual temperature outside is much colder than what the thermometer says if it is a windy day. The wind chill makes it colder than the thermometer reads. Using the formula below determine the wind chill temperature (w) if the thermometer reading ‘t ‘ reads 50°. 13 w = -22 + t 10
12.
Algebra 1 Unit 2
Moselle is riding a roller coaster that is 155 feet high. He is at the very top and he wants to know how far he is from the bottom after 2 seconds. Use the formula below to find out how far from the bottom he is. (s represents seconds) distance from bottom = 155 – 16s2
5
Unit 2 Worksheet 3 Solve the following: 1. 4x + 5x = 45
2.
3x + 2x + 6 = 71
3.
3x + 4x + 2 = –57 + 3
4.
6(x + 5) = 12
5.
4(2x – 7) = 12
6.
1 (6x + 18) = –24 3
7.
1 (4x + 6) = 0 2
8.
1 (12x – 4) = –13 4
9.
2 + 3(x – 5) = 5
10.
3 + 5(m – 3) = –2
11.
4 – (9g – 5) = – 18
12.
2x – 4(x – 1) = 10
13.
6 – 4(x + 2) = 9 – 35
14.
5 – 2(x + 6) = -15
15.
2 + 4(x – 2) + 6x = –96
16.
6 + 2(x – 5) + 4x = 44
17.
2(3x + 5) + 3(2x + 5) = 1
18.
–
19.
4 5x
20.
5 2(x 3)
x = –15
21.
2 4
22.
2 + 3 2(x
4)
7
8x + 2 = –18
(x 1)
Algebra 1 Unit 2
3x = 14
1 (6x – 4) + 5(x + 2) = 0 2
7 = 35
6
Unit 2 Worksheet 5 Write an algebraic word problem for the following and then solve. 1. The cost of renting a jet ski is $40 per day plus $50 per hour of use. How many hours was a jet ski rented if the total cost was $390?
2.
When an alligator is born it is about 8 inches long. Each year they grow about 12 inches. Determine how old an alligator is that is 116 inches long.
3.
Membership at the Healthy You Gym is a $40 initial fee and $5 a visit. If Sanjaya’s bill was $105, how many times had he visited the gym?
4.
Membership to a video game club is $50 a year and $3 per game rented. At the end of the year Harvey had spent $296. How many games had he rented?
5.
Danielle wants to paint a ceramic planter. The total price is the cost of the planter plus an hourly painting rate of $6. Determine how many hours Danielle painted if she spent $9 on the planter and her total bill was $33.
6.
Jackson Intermediate School is doing a fund raiser selling magazine subscriptions. The magazine publisher will pay the school a starting bonus of $500 and then $4 for each magazine subscription sold. At the end of the fund raiser the school is paid a total of $1360. How many subscriptions did they sell?
7.
The lengths of the sides of a triangle are x, 2x + 1, 5x + 4 inches. If the perimeter is 53 inches, what is the value of x ?
Algebra 1 Unit 2
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8.
The perimeter of the quadrilateral shown is 45 inches. Find the value of x .
x+6 2x – 1
5x + 4 4x
9.
The sides of a square are all the same length. If the perimeter 3x + 2 of the square shown below is 56 cm., find the value of x. 3x + 2 3x + 2 3x + 2
10.
The length of a rectangle is 50 cm. longer than the width. If the perimeter of the rectangle is 220 cm., find the width and length. x + 50 x
Unit 2 Worksheet 6 1. The sum of two consecutive integers is 143. What are the integers? 2. The sum of two consecutive odd integers is 72. What are the integers? 3. The sum of two consecutive integers is 65. What are the integers? 4. The sum of two consecutive even integers is 26. What are the integers? 5. The sum of two consecutive even integers is 214. What are the integers? 6. The sum of three consecutive even integers is 54. What are the integers? 7. The sum of three consecutive integers is 513. What are the integers? 8. The sum of three consecutive odd integers is 339. What are the integers?
Algebra 1 Unit 2
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Unit 2 Worksheet 7 Solve the following word problems by writing an equation and then solving algebraically. 1. Alison has a piece of board 70 inches long. She cuts it into three pieces. The longest piece is twice the length of the middle-sized piece, and the shortest piece is 10 inches shorter than the middle-sized piece. Find the length of the longest piece. (Let x = length of the middle-sized piece)
2.
During the 2007 baseball season, Wade was up to bat 10 more times than his teammate Dwight. Dwight batted 17 fewer times than another teammate, Ellis. The three players were up to bat a total of 1650 times. How many times did Ellis come to bat?
3.
There are a total of 20 lions, tigers and bears. If the number of tigers is 2 more than the number of lions and the number of bears is 1 more than the number of tigers, find the number of each.
4.
Debbie is one year older than Dave. James is twice as old as Dave. Joelle is twice as old as Debbie. Altogether their ages total 33. Find each person’s age. (Let x = Dave’s age)
Algebra 1 Unit 2
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5.
Tom performed a total of 100 hours of community service. He served at three charities – Salvation Army, Red Cross and Rescue Mission. The number of hours he served at the Red Cross was 19 hours more than at the Salvation Army. The number of hours he served at the Rescue Mission was 8 hours more than what he served at the Red Cross. Find the number of hours he volunteered at each charity.
6.
Rainbo Bread Company delivered a total of 180 loaves of bread to three markets. Savemart received 12 more loaves than Vons. Ralphs received 6 more loaves than Savemart. Find the number of loaves delivered to each market.
7.
Hungry Bear Cookies baked a total of 98 cookies of three kinds – chocolate chip, oatmeal raisin, and peanut butter. The number of oatmeal raisin was twice the number of peanut butter. The number of chocolate chip was 3 more than the number of oatmeal. Find the number of cookies of each type.
Algebra 1 Unit 2
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Unit 2 Review 1 Find the value of x in problems 1 – 10 1. 9x + 5 = 0
2.
3 x – 12 = 36 4
3.
7 – (x + 4) = 0
4. 2(x – 6) + 8 = 20
5.
4 + 2(x + 3) = 24
6.
4(2x – 3) – 9(x + 2) = 0
7.
12x – 36 = 3x
8.
7x + 23 = 3x – 29
9.
10.
2[6x – 5(x – 3)] + 4 = 40
4 + 4(x – 5) = 12x
Write an equation for each problem below and then solve it. 11.
The lengths of the sides of a triangle are 2x, x + 4, and 13 inches. If the perimeter of the triangle is 35 inches, what is the value of x?
12.
The cost to hire an electrician is $50 plus $65 per hour. How many hours did the electrician work if his bill was $505?
13.
A piece of string that is 132 inches long is cut into 3 pieces. The second piece of string is twice as long as the first piece. The third piece of string is three times as long as the first piece. Find the length of the longest piece of string.
14.
Three consecutive odd integers have a sum of 99. Find the three integers.
15.
A bakery makes three flavors of bagels – strawberry, cinnamon-raisin, and blueberry. This morning they made a total of 52 bagels. They made two more cinnamon-raisin than strawberry. The number of blueberry is 9 more than the number of cinnamon-raisin. How many of each flavor did they make?
In problems 16 – 18, write an equation and solve. 16. The grams of medicine (g) prescribed for a child weighing p pounds can be found using the equation g = 4 + 2w How much does a child weigh if he was prescribed 54 grams of medicine?
Algebra 1 Unit 2
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17.
The cost (c) in dollars to rent a chain saw for h hours is found using the equation c = 3h + 6 How much would it cost to rent the saw for 12 hours?
18.
A rock is thrown vertically upward into the air. The height (h) in feet of the rock after t seconds can be found using the equation h = –16t2 + 128t Find the rock’s height after 3 seconds.
Unit 2 Review 2 Select the correct multiple choice response: 1.
Max is solving the equation 3x – 2 = 10. Which of the following are the correct steps in finding the solution? 1 A. Multiply both sides by . Then subtract 2 from both sides. 3 1 B. Multiply both sides by . Then subtract 2 from both sides. 3 C. Subtract 2 from both sides. Then divide both sides by 3. D. Add 2 to both sides. Then divide both sides by 3.
2.
The solution of this equation has an error. Identify at which step the error occurred. 5x + 2 – 2x = 9 + 7 Step 1: 5x + 2 – 2x = 16 Step 2: 7x + 2 = 16 Step 3: 7x = 14 Step 4: x=2 A.
3.
Step 1
B.
Step 2
C.
Step 3
D.
Step 4
The solution of this equation has an error. Identify at which step the error occurred. 2(x + 4) + 6 = 14 Step 1: Step 2: Step 3: Step 4 A.
Step 1
Algebra 1 Unit 2
2x + 4 + 6 = 14 2x + 10 = 14 2x = 4 x=2 B.
Step 2
C.
Step 3
D. Step 4 12
4
Jason solved this equation as shown below:
Step 1: Step 2: Step 3:
x 3 x 3
4
5 2
4
7
x 3 3 x=1
Which statement is true about his solution? A. Jason solved it correctly. B. Jason made an error in step 1 C. Jason made an error in step 2 D. Jason made an error in step 3 5.
5 + 2(x + 3) = 17 is equivalent to which selection? A. 2x + 11 = 17 B. 2x + 8 = 17 C. 7x + 6 = 17 D. 7x + 3 = 17
6.
Which of the following is equivalent to A. 5x + 1 = 9 B. 5x + 4 = – 9 C. 6x + 3 = – 9 D. 6x + 1 = – 9
7.
Which statement is true? A. x + x = x2 B. x + x = 2x C. –x2 = x2 D.
x(
3(2x + 1) = – 9
?
1 )=x x
Algebra 1 Unit 2
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8.
A student worked the following problem: Solve:
8x + 10 – 6x + 4 = 24
Their work is shown below: Step 1 2x + 14 = 24 Step 2 2x = 38 Step 3 x = 19 Which statement is correct? A. There is an error in Step 1 B. There is an error in Step 2 C. There is an error in Step 3 D. No errors were made. The problem was worked correctly. 9.
Solve A. B. C. D.
for x: 5 –5 –7 7
3[4x – 2(x –6)] + 6 = 0
10.
Amy simplified the expression below. In which step did she first make a mistake? 2 + 3(1 + 4)
Step 1 Step 2 Step 3
11.
2 + 3 (5) 5 (5) 25
A. B. C. D.
Step 1 Step 2 Step 3 Amy did not make a mistake
Solve A. B. C. D.
for x: 22 –22 16 –16
Algebra 1 Unit 2
–7 – (x + 3) = 12
14
12.
13.
The total cost (c) in dollars to work on a computer at Kinkos for h hours is given by the equation c = 2h + 4 If Jeremiah worked on the computer for 12 hours, how much did it cost him? A. $4 B. $24 C. $2 D. $28 Solve for x: 6 – 2(x – 8) = 24 A. –1 B. 1 C. 14 D. –14
Select the correct multiple choice response: 14. Identify at which step the error occurred in solving the equation below: 6(x + 4) – 2 = 4x
A.
Step 1 Step 2 Step 3 Step 4
6x + 24 – 2 = 4x 6x + 22 = 4x 2x + 22 = 0 x = 11
Step 1
B.
Step 2
C.
Step 3
D.
Step 4
15.
Which is equivalent to
16.
A. 6x = –8 B. 6x = 6 C. 9x = 17 D. 9x = –39 Identify at which step the error occurred in solving the equation below:
A.
5 + 2(3x – 4) = 12x – 11
3 4(x 2) 10
= 14
Step 1 Step 2 Step 3 Step 4 Step 5
12(x – 2) – 10 12x – 24 – 10 12x – 34 12x x
= 14 = 14 = 14 = 48 = 4
Step 1
B.
Algebra 1 Unit 2
Step 2
C.
Step 3
D.
Step 4 15
17.
18.
19.
The perimeter of the rectangle shown is 80 inches. Which equation could be used to represent this? x + 10 A. (x) + (x + 10) = 80 B.
x(x + 10) = 80
C.
(x) + (x + 10) + (x) + (x + 10) = 80
D. x + 10 = 80 The sum of 3 consecutive integers is 45. Which equation represents this? A. (x) + (x) + (x) = 45 B. (x) + (x + 1) + (x + 2) = 45 C. (x) + (x + 2) + (x + 4) = 45 D. (x) + (x + 1) + (x + 3) = 45 Jordan is going bowling. He must rent shoes for $3 and then pay $5 for each game bowled. Which equation represents this if ‘g’ represents the number of games bowled and ‘C’ represents cost. A.
20.
x
C = 3g + 5g
C. C = 3 + 5g The equation
Step 1 Step 2 Step 3
B. 3(x – 5) = 3x – 15 = 3x = x =
C = 3g + 5
D. C=8+g 60 is solved as follows: 60 75 25
What property was used to go from step 1 to step 2?
21.
A.
The multiplicative inverse property
B.
The additive inverse property
C.
The distributive property
The equation
Step 1 Step 2 Step 3
5x + 10 + 5 = 5x + 15 = 5x = x =
40 is solved as follows: 40 25 5
What property was used to go from step 2 to step 3? A.
The multiplicative inverse property
B.
The additive inverse property
C.
The distributive property
Algebra 1 Unit 2
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