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Algebra I Unit 1 Solving Single-Variable Equations and inequalities Unit Vocabulary Coefficient Constant Equation Exponent Expression Inequality Irrational numbers Linear Literal equation Non-Linear Products of Factors Rational Numbers Term Variable Lesson 1 Solving One- Step Linear Equations Solve each equation; be sure to check your solution. 2 1 1. X – 10 = 4 3. = 𝑚 − 5 2. - 6 = k – 6 5 4. n – 3.2 = 5.6 1 5. 16 = m – 9 6. x + 7 = 9 Algebra I Unit 1 7. 0.7 = r + 0.4 1 8. 𝑑+2=1 9. –8+b=2 3 5 10. – 4 + 𝑧 = 4 𝑘 11. – 4 = −5 12. 𝑚 3 = 1.5 13. 7x = 56 Solving Single-Variable Equations and inequalities 14. 13 = -26w 15. 16 = 4c 16. 0.5y = -10 5 17. 9 𝑣 = 35 5 18. 4 = 3𝑦 2 4 19. 6 𝑗= 2 3 21. 3 1 16 = 𝑧 8 22. −4.8𝑣 = −6𝑣 23. 1 = 𝑘 − 8 24. 𝑢 − 15 = -8 25. 𝑡 + 25 = −5 1 2 26. – 6 + ℎ = 3 1 27. 2 = 𝑑 + 4 𝑐 20. 8 = 7 2 Algebra I Unit 1 3 1 4 4 28. 1 = − + 𝑤 29. 31. 4x = 28 34. 32. 84 = -12a 𝑘 =8 4 30. 6 = Solving Single-Variable Equations and inequalities 𝑡 −3 8 1 𝑟=9 4 35. 10 = 5 𝑦 33. ½ d = 7 5 36. 15 = 6 𝑦 −5 Lesson 2 Solving Multi-Step Linear Equations Solve each equation; be sure to check your solution. 1. 10 – 6 – 2x 3. 1.5 = 1.2y – 5.7 2. -4 + 7x = 3 4. 𝑛 7 +2=2 3 5. 6. 𝑞 15 2𝑥 5 1 3 −5=5 1 −2=5 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 7. 6𝑥 + 3 − 8𝑥 = 13 12. 4(x -2) + 2x = 40 17. 6h – 17 = 17 8. 8x – 21 – 5x = -15 13. -2(3 – d) = 4 18. 0.6v + 2.1 = 4.5 9. 10 – (4y + 8) = -20 14. 2 (2𝑥 − 4) = 12 10. 9 = 6 – ( x + 2) 11. 2a + 3 – 8a = 8 1 19. 3x + 8 = 18 3 20. 0.6g + 11 = 5 15. 4 (𝑥 − 12) = −4 16. 5 = 2g + 1 4 21. 32 = 5 – 3t Algebra I Unit 1 1 3 5 5 22. 2𝑑 + = 1 23. 1 = 2𝑥 + 2 𝑧 3 24. 2 + 1 = 2 2 25. 3 = 3 4𝑗 Solving Single-Variable Equations and inequalities 1 𝑥 2 5 5 5 27. − = − 28. 6 = -2(7 – 2c) 32. 2(x + 3) = 10 33. 17 = 3(p-5) + 8 2 29. 5(h – 4) = 8 34. 3 (6𝑥 − 12) = 18 30. -3x – 8 + 4x = 17 35. 5(1 – 2w) + 8w = 15 31. 4x + 6x = 30 36. 4x + 7 – x = 19 6 3 3 26. 4 = 8 𝑥 − 2 5 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 𝑐 37. 3( x – 4) = 48 39. 15 = 3 − 2 41. 5x + 9 = 36 38. 17 = x – 3(x + 1) 40. 2x + 6.5 = 15.5 42. 3.9w – 17.9 = -2.3 Lesson 3 Solving Linear Equations with Variables on Both Sides 1. 7k = 4k + 15 3. 4b + 2 = 3b 5. 2(y + 6) = 3y 2. 5x – 2 = 4x + 4 4. 0.5 + 0.3y = 0.7y – 0.3 6. 2k – 5 = 3(1 – 2k) 6 Algebra I Unit 1 7. 3 – 5b + 2b = -2 – 2(1 – b) 8. 1 2 3 ( 𝑏 + 6) = 𝑏 − 1 2 9. 3𝑥 + 15 − 9 = 2(𝑥 + 2) 10. 7n – 2 = 5n + 6 Solving Single-Variable Equations and inequalities 11. 4 – 6a + 4a = -1 -5(7 – 2a) 15. 2c + 7 + c = -14 + 3c + 21 12. x + 4 – 6x = 6 - 5x – 2 16. 2c – 5 = c + 4 13. -8x + 6 + 9x = -17 + x 17. 8r + 4 = 10 + 2r 14. 4y + 7 – y = 10 + 3y 18. 7x – 4 = -2x + 1 + 9x - 5 7 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 19. 2x – 1 = x + 11 23. 3c – 4c + 1 = 5c + 2 + 3 27. 5 – (t + 3) = -1 + 2(t – 3) 20. 28 – 0.3 y = 0.7y – 12 24. 6y = 8 – 9 + 6y 28. 7a – 17 = 4a + 1 21. 8x + 6 – 9x = 2 – x - 15 25. 5 + 3(q – 4) = 2( q + 1) 29. 2b – 5 = 8b + 1 22. -2(x + 3) = 4x – 3 26. 6 – 2x – 1 = 4x + 8 – 6x - 3 30. 4x – 2 = 3x + 4 8 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 31. 2x – 5 = 4x -1 33. 5x + 2 = 3x 35. 5 – (n – 4) = 3(n + 2) 32. 8x – 2 = 3x + 12.25 34. 3c – 5 = 2c + 5 36. 6(x + 7) – 20 = 6x Lesson 4 Solving Literal Equations Solve each equation for the indicated variable. 1. d = rt (r) 3. F = I – gt 9 2. F = 5 𝐶 + 32 (𝐶) 4. S = 𝑤−10𝑒 𝑚 9 (i) 5. M – n = 5 (w) 6. 𝑚 𝑘 =𝑥 (m) (𝑘) Algebra I Unit 1 7. 5 − 𝑏 = 2𝑡 8. 𝐷 = 𝑚 𝑣 9. C = 𝜋𝑑 (𝑡) (𝑣) 𝑚𝑠−𝑤 (𝑚) −10 12. pq = x (q) 𝑚 13. V = lwh (w) 14. St + 3t = 6 15. M – 4n = 8 (𝑑) 10. A = ½ bh (h) 11. e = Solving Single-Variable Equations and inequalities 16. 𝑓+4 𝑔 (s) (m) (𝑓) =6 17. 𝑏 + 𝑐 = 19. 𝑛 = 𝑝 − 6 (𝑛) 10 𝑎 18. xy – 5 = k 10 (𝑎) (x) 20. 𝑥−2 𝑦 =𝑧 (𝑦) 21. 𝑠 = 180𝑛 − 360 (n) 𝑥 22. 5 − 𝑔 = 𝑎 1 23. 𝐴 = 2 𝑏ℎ 24. y = mx + b (𝑥) (𝑏) (x) Algebra I 25. a = 3n + 1 Unit 1 (n) Solving Single-Variable Equations and inequalities 26. PV = nRT (T) 27. 3x + 4y = 2 (y) Lesson 5 Real-World Applications Involving Linear Equations in One-Variable Write an equation using the given information and solve for the indicated variable. Be sure to show all work and explain what your answer represents. 1. Mr. Skipper’s classroom had too many desks in it so he removed the 12 desks that were broken to create more space. He now has 18 desks in his classroom. How many desks did he originally have? 4. The long-distance rates of two phone companies are: Company A $0.36 plus $0.03 per minute and Company B $0.06 per minute. How long is a call that costs the same amount no matter which company is used? What is the cost of that call? 2. A 130 – pound woman burns 9.83 calories per minute while running. She burns 3.25 calorie per minute while walking during her cooldown. She runs for t minutes and exercises for a total of 45 minutes. How many calories , to the nearest tenth, does she burn if she runs for 35 minutes ? 5. Paul bought a student discount card for the bus. The card costs $7 and allows him to buy daily bus passes for $1.50. After one month, Paul spent $29.50. How many daily bus passes did Paul buy? 6. Jennifer is saving money to buy a bike. The bike costs $245. She has $125 saved, and each week she adds $15 to her savings. How long will it take her to save enough money to buy the bike. 3. Grant has 5 short sleeve shirts and some long sleeve shirts. All together he has 9 shirts. How many long sleeved shirts does he have? 11 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 7. Drew’s grandmother had money to spend evenly on her 4 grandchildren for presents. She spent $60 on each grandchild. How much money did Boudreaux’s grandmother have before she bought the presents? 11. A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which both companies will charge the same amount? What will the cost be? 8. Four times Greg’s age, decreased by 3 is equal to 3 times Greg’s age, increased by 7. How old is Greg? 12. In 2003, the population of Zimbabwe was about 12.6 million, which was 1 million more than 4 times the population in 1950. What is the population of Zimbabwe in 1950? 9. Mrs. Jackson’s classroom has some rows with 4 desks and the same amount of rows with 5 desks in them. She has a total of 27 desks. How many rows does Mrs. Jackson have in her classroom with 4 desk in them? How many rows does Mrs. Jackson have in her classroom with 5 desk in them? 10. Sarah ended up with $240 in her savings account at the end of the summer, which is twice the amount she started with at the beginning of the summer. How much money was originally in her savings account at the beginning of the summer? 13. Alex belongs to a music club. In this club, students can buy a student discount card for $19.95. This card allows them to buy CDs for $3.95 each. After one year, Alex has spent $63.40. Write and solve an equation to find how many CDs Alex bought this year. 14. Luis deposited $500 into his bank account. He now has $4732in his account, how much was in his account before the deposit. 12 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 15. Tyrone spends nine dollars to get into the movie theatre plus six dollars every time he visits the concession stand. He spent a total of thirty-three dollars at the movie theatre. How many visits did Tyrone make to the concession stand? 20. Emily ended up with $540 in her savings account at the end of the summer, which is $50 more than twice the amount she started with at the beginning of the summer. How much money was originally in her savings account at the beginning of the summer? 7 16. After taxes Forest’s take-home pay is 10 of his salary before taxes; what is Forest’s salary before taxes for the pay period that resulted in $392 of take-home pay. 21. Jon and Sara are planting tulip bulbs. Jon has planted 60 bulbs and is planting at a rate of 44 bulbs per hour. Sara has planted 96 bulbs and is planting at a rate of 32 bulbs per hour. In how many hours will Jon and Sara have planted the same number of bulbs? How many bulbs will that be? 17. Sara paid $15.95 to become a member at a gym. She then paid a monthly membership fee. Her total cost for 12 months was $735.95. How much was the monthly fee? 22. The Baseball Birthday Package at a park cost $192; this includes tickets, drinks, and cake for a group of 16 children. How much does it cost for each child? 18. Kate is saving to take an ACT prep course that costs $350. So far, she has saved $180, and she adds $17 to her savings each week. How many more weeks must she save to be able to afford the course? 23. Max lost 23 pounds while on a diet. He now weighs 184 pounds; how much did Max initially way? 19. Lisa earned $6.25 per hour at her after-school job. Each week she earned $50, how many hours does she work each week? 24. Over 20 years, the population of a town decreased by 275 people to a population of 850 people; what was the original population of the town 13 Algebra I Unit 1 Solving Single-Variable Equations and inequalities Lesson 6 Solving One-Step Linear Inequalities in One- Variable Solve the following inequalities and graph the solutions. 1. X + 9 < 15 7. -8x > 72 2. d – 3 > -6 8. -50 ≥ 5𝑞 3. 0.7n ≥ 𝑛 − 0.4 9. 4. 3x > -27 5. 2 3 𝑟<6 6. 4𝑘 > 24 3 4 𝑔 > 27 13. 7x > -42 𝑥 14. −3 ≤ −5 15. x + 12 < 20 10. s + 1 ≤ 10 16. d - 0 5 > -7 11. q – 3.5 < 7.5 17. 2.4 ≤ 1 12. 2 2 > −3 + 𝑡 14 𝑚 3 18. 0.9 > n – 0.3 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 19. 12 < p + 6 23. 10 > -2x 27. -40 > 8b 20. ¾ r < 12 24. -5 + x 6 28. 4.25 > -0.25h 21. w + 3 > 6 25. 12 . −6 22. 3b > 27 29. z – 2 > -11 𝑡 30. 4 > -8g 26. -5 + x < -20 Lesson 7 Solving Multi-Step Linear Inequalities in One- Variable Solve the inequalities and graph the solutions. 1. 160 + 4f < 500 3. -12 > 3x + 6 2. 7 – 2t < 21 4. 15 𝑥+5 −2 >3 Algebra I 5. Unit 1 1−2𝑛 3 Solving Single-Variable Equations and inequalities 10. 3 + 2( x + 4) > 3 ≥7 5 3 1 6. – 4 + (−8) < −5𝑐 − 2 11. 7. −3(3 – x) < 42 12. 45 + 2b > 61 8. 9. 4 5 1 < 8𝑥 −4 8 13. 8-3y > 29 3 𝑥+2>5 14. 2 – (-10) > -4t 2m + 5 > 52 16 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 15. -4(2 – x) < 8 16. 2 1 20. 4c – 7 > 5 1 21. 𝑓+2>3 3 4+𝑥 3 > −4 17. 2m + 1 > 13 22. 1 < 0.2x – 0.7 18. 2d + 21 < 11 23. 19. 6< -2x + 2 3−2𝑥 3 ≤7 24. 2𝑥 + 5 ≥ 2 17 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 25. 4( x + 2) > 6 26. 1 2 30. 3(j + 41) < 35 31. 4r – 9 > 7 3 𝑥+3<4 4 32. 3< 5 – 2x 27. 4 – x + 62 ≥ 21 28. 33. 4 – x > 3 ( 4-2) 𝑤+3 2 >6 34. 11w + 99 < 77 29. 0.2 ( x – 10) > -1.8 18 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 38. f + 2 ½ < -2 1 35. 9 ≥ 𝑣 + 3 2 39. -2 > 7x – 2 (x – 4) 36. -4x – 8 > 16 40. 2 37. 8 − 3 𝑧 ≤ 2 3𝑛−8 5 ≥2 Lesson 8 Solving Linear Inequalities in One-Variable with Variables on Both Sides Solve each inequality and graph the solutions. 1. x< 3x + 8 3. 6(1-x) < 3x 2. 6x – 1 < 3.5x + 4 4. x + 5 > x + 3 19 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 5. 2(x+3) < 5 + 2x 10. x – 2 < x + 1 6. y < 4y + 18 11. 2(k – 3) > 6 + 3k – 3 7. 4m – 3 < 2m + 6 12. 0.9y > 0.4y – 0.51 8. 4x > 7x + 6 13. 4( y-1) > 4y + 2 9. 5t + 1 < -2t – 6 14. 1.6x < -0.2x + 0.9 20 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 15. 2x – 7 < 5 + 2x 20. 4v + 1 < 4v -7 16. 2(3y – 2) – 4 > 3(2y + 7) 21. 7y + 1 < y – 5 17. 5(2 – r) > 3(r – 2) 22. 27x + 33 > 58x – 29 18. 0.5x – 0.3 + 1.9x < 0.3x + 6 23. -3r < 10 – r 19. 2x >4x – 6 24. 2(x-2)< -2( 1-x) 21 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 25. 5c – 4 > 8c + 2 30. 2(6 – x) < 4x 26. 4.5x – 3.8 > 1.5x – 2.3 31. 4x > 3( 7 – x) 27. 4(y + 1) < 4y + 2 32. 28. 5(4 + x) < 3(2 + x) 1 2 3 1 𝑓 + 4 ≥ 4𝑓 33. -36.72 + 5.65t < 0.25t 29. -4 (3 – p) > 5( p + 1) 34. b – 4 > b - 6 22 Algebra I Unit 1 Solving Single-Variable Equations and inequalities Lesson 9 Real- World Applications Involving Linear Inequalities in One Variable Use the given information to write an inequality, solve the inequality and graph the inequality. 1. The memory in Tenea’s camera phone allows 6. Mrs. Lawrence wants to buy an antique bracelet her to take up to 20 pictures. Tenea has already at an auction. She is willing to bid no more than taken 16 pictures. How many more pictures can $550. So far, the highest bid is $475 Write and Tenea take? solve an inequality to determine the amount Mrs. Lawrence can add to the bid. 2. The Daily Info Newspaper charges a fee of $650 plus $80 per week to run an ad. The People’s Paper charges $145 per week. For how many weeks will the total cost at Daily Info be less expensive than the cost at People’s Paper? 3. Sami has a gift card. She has already used $14 of the total value, which was $30. How much more can she spend? 4. To win the blue ribbon for the Heaviest Pumpkin Crop at the county fair, the average weight of John’s two pumpkins must be greater than 819 pounds. One of his pumpkins weighs 887 pounds. What is the least number of pounds the second pumpkin could weigh in order for John to win the blue ribbon? 5. Ryan has a $16 gift card for a health store where a smoothie costs $2.50 with tax. What are the possible numbers of smoothies that Ryan can buy? 7. A 15-foot tall cedar tree is growing at a rate of 2 feet per year beneath power lines that are 58 feet above the ground. The power company will have to prune or remove the tree before it reaches the lines. How many years can the power company wait before taking action? 8. TO rent a certain vehicle, Rent-A-Ride charges $55.00 per day with unlimited miles. The cost of renting a similar vehicle at We Got Wheels is $38.00 per day plus $0.20 per mile. For what number of miles is the cost at Rent-A-Ride less than the cost as We Got Wheels? 9. A particular type of contact lens can be worn up to 30 days in a row. Alex has been wearing these contact lenses for 21 days. How many more days can Alex wear his contact lenses? 10. A pitcher holds 128 ounces of juice. What are the possible numbers of 10-ounce servings that one pitcher can fill? 23 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 11. A sales representative is given a choice of two paycheck plans. One choice includes a monthly base pay of 4300 plus 10% commission on his sales. The second choice is a monthly salary of $1200. For what amount of sales would the representative make more money with the first plan? 12. The average of Jim’s two test scores must be at least 90 to make an A in the class. Jim got a 95 on his first test. What scores can Jim get on his second test to make an A in the class? 13. A-Plus Advertising charges a fee of $24 plus $0.10 per flyer to print and deliver flyers. Print and More charges $0.25 per flyer. For how many flyers is the cost at A-Plus Advertising less than the cost at Print and More? 14. Jill has a $20 gift card to an art supply store where 4ox tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy? 15. One cell phone company offers a plan that costs $29,99 and includes unlimited night and weekend minutes. Another company offers a plan that costs $19.99 and charges $0.35 per minute during nights and weekends. For what numbers of night and weekend minutes does the second company’s plan cost more than the first company’s plan? 16. Marcus has accepted a job selling cell phones. He will be paid $1500 plus 15% of his sales each month. He needs to earn at least $2430 to pay his bills. For what amount of sales will Marcus be able to pay his bills? Extra Practice Unit 1 Solve each equation for the missing value; be sure to check your answer. 1. -4x + 7 = 11 3. 3m – 10 = 2(4m – 5) 5. -17 – 2x = 6 – x 2. x – (-3) = 12 4. 17 = 5y – 3 24 6. p – 5 = 12 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 7. 3(t – 1) = 9 + t 12. -13 = -h – 7 17. 2(𝑥 + 4) = 3(𝑥 − 2) 8. -4 = 2p + 10 13. 5 – x-2= 3 + 4x + 5 18. −2(x – 10) = 7 9. 3m + 4 = 1 14. −6 = 5 + 4 10. -2x = 16 11. 12.5 = 2g – 3.5 𝑦 7 1 20. 8 = 4(𝑞 − 2) + 4 2 21. −2h = 18 15. 9 = 2𝑛 + 9 4 1 19. 2 (𝑏 − 4) = -6 2 16. − 5 + 5 = 3 25 Algebra I Unit 1 Answer the following question. 22. For her cellular phone service, Vera pays $32 a month, plus $0.75 for each minute over the allowed minutes in her plan. Vera recieved a bill for $47 last month. Write and solve an equation that shows how many minutes did she use her phone beyond the allowed minute. Solving Single-Variable Equations and inequalities 27. Justin and Tyson are beginning an exercise program to train for football season. Justin weighs 150lb and hopes to gain 2lb per week. Tyson weighs 195 lb and hope to lose 1lb per week. If the plan works, in how many weeks will the boys weigh the same amount? What will that weight be? 23. Over 20 years, the population of a town 28. A full year membership to a gym costs $325 decreased by 275 people to a population of 850. upfront with no monthly charges. A monthly Write and solve an equation to find the original membership cost $100 upfront and $30 per population. month. For what numbers of months is it less expensive to have a monthly membership? 24. The Home Cleaning Company charges $312 to power-wash the siding of a house plus $12 for each window. Power Clean charges $36 per 29. Stephen belongs to a movie club in which he window, and the price includes power-washing pays an annual fee of $39.95 and then rents the siding. How many windows must a house DVDs for $0.99 each. In one year, Stephen spent have to make the total cost from The Home $55.79. Write and solve an equation to find how Cleaning Company less expensive than Power many DVDs he rented. Clean? 25. 𝐸𝑎𝑟𝑡ℎ 𝑡𝑎𝑘𝑒𝑠 365 𝑑𝑎𝑦𝑠 𝑡𝑜 𝑜𝑟𝑏𝑖𝑡 𝑡ℎ𝑒 𝑆𝑢𝑛. Mars 30. Tom saved $550 to go on a school trip. The cost takes 687 days to orbit the sun. Write and solve for a hotel room, including tax, is $80 per nice. an equation to find how many more days Mars What are the possible nights Tom can stay at takes than Earth to orbit the Sun. the hotel? 26. Maggie’s brother is three years younger than twice her age. The sum of their ages is 24. Write 31. Josh can bench press 220 pounds. He wants to and solve an equation that shows how old bench-press at least 25 pounds. Write and solve Maggie is. an inequality to determine how many more pounds Josh must lift to reach his goal. 26 Algebra I Unit 1 Solving Single-Variable Equations and inequalities Solve each equation for the indicated variable. 32. ax + r = 7 (r) 34. 2a + 2b = c (b) 33. 5p + 9c = p (c) 36. 35. P = 4s (s) Solve each inequality and graph the solution 38. 𝑎 − 3 ≥ 2 39. 3(x-5) >3x 𝑎 42. 2.5 > q – 0.8 2 44. 3𝑥 ≤ 5𝑥 + 8 41. -5 > -5 – 3w 45. 10 > 27 𝑗 = 𝑘 (𝑗) 37. 𝑏 = 𝑐 (𝑏) 43. 3 𝑘 > 6 40. 1.1 m < 1.21 ℎ−4 5−3𝑝 2 Algebra I Unit 1 Solving Single-Variable Equations and inequalities 46. -45 + x < -30 51. 2v + 1 >2 47. -25 > 10p 1 1 3 3 52. 𝑟 + 4 ≤ 4 48. 2k + 7 > 2(k + 14) 53. 9𝑦 + 3 > 4𝑦 − 7 49. -18 > 33 – 3h 54. 4 ( 𝑥 + 3) > −24 50. 1.5x – 1.2 < 3.1x – 2.8 28