Period: _____ Solve each equation. 1) + 7

Algebra I: Chapter 1 Review

Name: __________________________ Period: _____

Solve each equation. 1) 𝑝 + 7 = −9

2) −10.5 = 𝑤 + 3.5

3) 𝑠 − (−12) = 15

4) 𝑞 − 9 = −14

5)

𝑧 −2

6)

𝑘 3

=7

=4

7) −32 = 4𝑦

8) 4𝑣 = 48

Write and solve an equation to answer the question. 9) The width of a laptop is 11.25 inches. The width is 0.75 times the length. What is the length of the laptop?

10) The population of a city is 645 people less that it was 5 years ago. The current population is 13,500. What was the population 5 years ago?

Solve each equation. 11) 0.5ℎ + 7 = 10

12) −0.5𝑝 − 2.5 = 9

13) −43 = 12 − 6𝑝 + 𝑝

15) 12 − 5(3𝑟 + 2) = 17

14) −11𝑗 − 6 + 3𝑗 = −30

16) 3(𝑥 − 2) + 5(2 − 𝑥) = 16

Write and solve an equation to answer the question. 17) You purchase two bottles of sunscreen and a hat. The hat costs $6.50. You pay 6% sales tax. You pay a total of $16.43. How much does one bottle of sunscreen cost?

18) The perimeter of a patio is 64 feet. The width of the patio is 12 feet and the length of the patio is (𝑥 + 6) feet. What is the length of the patio?

Solve each equation. 19) 4𝑥 − 7 = −3𝑥

20) 5𝑡 + 7 = 3𝑡 − 9

2

21) 3 (3 − 6𝑥) = −3(8𝑥 − 4)

3 4

22) (12𝑐 − 4) = 15(𝑐 + 1)

23) −3(𝑤 + 4) = 4𝑤 − 5

25) 2(3𝑥 + 6) = 3(2𝑥 − 6)

24) 3(7𝑟 − 2) = 21𝑟 − 6

26) 10𝑓 + 15 = 2(5𝑓 − 1)

Write and solve an equation to answer the question. 27) One serving of oatmeal provides 16% of the dietary fiber you need daily. You must get the remaining 21 grams of dietary fiber from other sources. How many grams of dietary fiber to you need daily?

28) Pizza A charges $10 for a cheese pizza and $1.50 per topping. Pizza B charges $12.50 for a cheese pizza and $1.00 per topping. When would you pay the same amount for Pizza A and Pizza B?

Solve each equation. 29) |𝑏 − 2| = 5

31) |𝑥 + 4| + 7 = 3

30) |𝑘 + 6| = 9

32) |8𝑦 − 3| = −13

33) |𝑥 − 3| + 9 = 30

38) |5𝑟 + 3| = 2𝑟

34) |3𝑥 − 6| − 9 = −3

39) |2𝑗 + 3| = |𝑗|

35) −4|5𝑔 − 12| = −12

40) |3𝑓 − 6| = |9𝑓|

36) 7|2𝑐 − 6| + 4 = 32

41) |𝑏 + 3| = |2𝑏 − 2|

37) |2𝑦 + 5| = 3𝑦

42) |9𝑤 − 4| = |2𝑤 + 10|

Write an absolute value equation to find the minimum and maximum values. 43) For a writing assignment, the essay should be at least 375 words but no more than 425 words.

44) The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.

Solve each literal equation for 𝒙. 45) 4𝑥 + 𝑦 = 8

47) 𝑤 = 4𝑎𝑥 − 9𝑥

46) 8𝑥 + 2𝑦 = 18

48) 𝑧 = 6𝑥 + 𝑦𝑧

Use the simple interest formula, 𝑰 = 𝑷𝒓𝒕. 49) You deposit $1500 in a savings account that earns simple interest at an annual rate of 3%. How long must you leave the money in the account to earn $900 interest?

50) You deposit $800 in a savings account that earns simple interest at an annual rate of 5%. How long must you leave the money in the account to earn $100 interest?

1)

2) 𝑝 = −16

6)

3) 𝑤 = −14

7) 𝑘 = 12

11) 16)

𝑦 = −8

17)

26) 31)

36) 𝑐 = 1,5 41)

𝑦=5 42)

1 𝑏 = − ,5 3 46)

6 𝑤 = − ,2 11 47)

1 9 𝑥 =− 𝑦+ 4 4

𝑤 𝑥= 4𝑎 − 9

No solution 30)

𝑏 = −3, 7 34)

𝑥 = −18, 24 38)

𝑡 = −8 25)

29)

33)

37)

20)

Infinitely many solutions

5 toppings

No solution

𝑟 = −1

𝑥=1 24)

28)

32) No solution

19)

𝑤 = −1

25 grams

12,855 people 15)

𝑗=3

20 feet 23)

27) No solution

15 inches

𝑝 = 11

𝑐 = −3

𝑧 = −14 10)

14)

18)

22) 1 𝑥= 2

𝑞 = −5

𝑣 = 12

$4.50

5)

9)

13) 𝑝 = −23

𝑥 = −6 21)

𝑠=3 8)

12) ℎ=6

4)

𝑘 = −15, 3 35) 9 𝑔 = ,3 5

𝑥 = 0,4 39)

40) 𝑗 = −3, −1

No solution

𝑓 = −1,

43) |𝑥 − 400| = 25

44) |𝑥 − 430| = 20

45)

48)

49)

50)

𝑧 − 𝑦𝑧 𝑥= 6

20 years

1 2

1 𝑥 =− 𝑦+2 4 2.5 years