6) = 7) 2.1 x 2.1 x 2.1 = 8) 0.75 x 0.75 = Expressions & Equations: HW # 47. Name: Date: Period:

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1 Expressions & Equations: HW # 47 For questions #1-8 write the expression in either exponential or expanded form. Example: = 5 5 1) = 3) 8 3 = 4) 10 6 = 5) g 4 = 6) = 7) 2.1 x 2.1 x 2.1 = 8) 0.75 x 0.75 = 9) Fill in the missing expression for each row. For whole number and decimal bases, use a calculator to find the standard form of the number. For fraction bases, leave your answer as a fraction. Exponential Form 3 2 Written as a Multiplication Expression Having Repeated Factors Standard Form 3 x x 2 x 2 x 2 x 2 x x x 1.5

2 Expressions & Equations: HW #48 Evaluate each expression. 1) ) ) 2 + (9 2 4) 4) 2 ( (3+4)) 5) ) ($ $ $0.05) 24 7) Consider a family of 4 that goes to a soccer game. Tickets are $5.00 each. The mom also buys a soft drink for $2.00. How would you write this expression?

3 Expressions & Equations: HW #49 1) Jill is packing a moving truck. She can pack each layer with 7 boxes long and 7 boxes wide. The truck height is 7 layers tall. How many boxes can she pack in the truck? Circle the correct answer. a) 7 boxes b) 21 boxes c) 49 boxes d) 343 boxes 2) What is the difference between 3g and g 3? 3) Tickets to a play cost $10 for members and $24 for non-members. Write an expression to find the total cost of 4 nonmember tickets and 2 member tickets. Then find the total cost. 4) Arleta is 2 years younger than Josh, and Josh is 5 years older than Monica, who is 9 years old. Which expression could you use to find Arleta s age? a) b) c) d) ) Write each expression using an exponent. 7 x 7 x x 1 3 x 1 3 x x ) Evaluate each expression. 8 x (2 4 3) + 8 (2 6) + (8 4) + 1

4 Expressions & Equations: HW #50 1) Complete the table below. The quotient of a number and 2 X 2 The sum of 8 and a number X + 9 One third of a number x 5 7 x the product of 12 and a number half a number one number plus 25 a number divided by 6 Write the algebraic expression. 2) Three carnival tickets cost c cents. What is the cost one? 3) Bob had 5 apples. His mom gave him a few more apples to share with his friends. How many apples does Bob have? Evaluate the following expressions using the values given. 4) 2c + d c = 3 d = 2 5) 4n 3d n = 2 d = 5 6) 3b + 2b² b = 4

5 Expressions & Equations: HW #51 Evaluate the following expressions if m = 4, z = 9, and r = ) 3 + m 2) z m 3) 12r 4) 60r 4 5) 4m 2 Use the tables below to answer questions 6-8. Admission Cost Adults (ages 19+) $12.50 Youth (ages 2-18) $7.50 Admission and Movie Pass Cost Adults (ages 19+) $18.50 Youth (ages 2-18) $13.50 Family Night Prices Cost (After 5pm on Friday) Individual Admission (all ages) $7.00 Individual Movie Pass (all ages) $7.50 6) What is the total cost for one individual admission and one individual movie pass on family night? 7) The expression 14.50x can be used to find the total coast for x tickets on family night for admission and the movie. What is the cost for 3 tickets? 8) Write an expression to find the cost of t youth tickets (admission only) and 4 individual admissions (family night).

6 Expressions & Equations: HW #52 Simplify: 1) s - 3s 2) y + 2y + 9 3) 3( 4g + 6) 4) 9m - 7m + 6n 5) 4 + 5y + 9y + 6 6) 4f f + 3g 7) 4(5x + 3) - 7 8) 8(4 + 7k) 9) 5 + 2(7 + 4r) 10) 5-3r + 4r 11) Factor each expression. Hint: Pull out the GCF! x ( + ) 4x + 40 ( + ) 12) Use the distributive property to rewrite the following expressions. 2( x + 3) 8( x - 6)

7 Expressions & Equations: HW #53 1) Factor each expression. Hint: Pull out the GCF! x ( + ) 7x + 28 ( + ) 2) Use the distributive property to rewrite the following expressions. 9( x + 8) 6( x - 5) 5(12 + x) 3) Simplify the following expressions. 7b + 8n 4b 8 + n 4x + 2x + 7x 5y + 7x x + 2 4s d + 3s y 34y + x + x

8 Expressions & Equations: HW #54 Quiz Review Fill in the blank with the correct vocabulary term from the box below. Inverse Operation Variable Term Algebraic Equation Algebraic Expression Expression Coefficient Equation 1) A letter that stands for a number. 2) A mathematical phrase containing variables, numbers, and operation symbols ex. 4x + 5 3) A number, variable, product, or a quotient in an expression. 4) A mathematical sentence that contains numbers, operation symbols, and an equal sign ex = 7 5) A mathematical phrase containing numbers and operation symbols ex. 6(5 3) 6) Operations that undo each other. 7) A mathematical sentence containing variables, numbers, operation symbols, and an equal sign. 8) The numerical factor in a term with a variable. Solving Algebraic Expressions - Substitute in for the variable and simplify the expression. 9) 7x + c 3 c = 5, x = 6 10) 65 d h d = 5, h = 6 Translating Expressions and Equations - Write an expression for the following phrases or sentences. 11) Subtract twenty from a number 12) A number plus thirteen is fifty-seven 13) Seven increased by y is twenty-four 14) The quotient of thirty-six and a number

9 Using the Distributive Property 15) 9(2 + 7b) 16) (5j + 3b)3 17) x 18) 18x + 6 ( + ) ( + ) Combining Like Terms 19) 17x + 8y + 9x 20) a a a a 21) 6 + 7t + 4 2t 22) 5y + 3x x + y ) 14t t 18 24) 10x x 5

10 Expressions & Equations: HW #55 1) Solving Equations - Use inverse operations to solve and check the following equations. y + 7 = 10 y + 7 = = 6 + e 10 = 6 + e t 7 = 12 t 7 = 12 z 6.3 = 2.1 z 6.3 = 2.1 2) Which of the following is true concerning x 5 = 13? a) To find the value of x, add 5 to each side. b) To find the value of x, subtract 5 from each side. c) To find the value of x, add 13 to each side. d) To find the value of x, subtract 13 from each side.

11 3) Alejandro is repairing a stained glass window. He needs to take it apart to repair it. Before taking it apart he makes a sketch with angle measures to put it back together. Write an equation and use it to determine the measure of the unknown angle.

12 Expressions & Equations: HW #56 1) Solve each equation, and check your solution f = f = 65 x 23 = 72 x 23 = 72 2) Translating & Solving Equations Write an equation with a variable for each of the problems below. Then use inverse operations to solve and check. The first problem has been started for you. April paid $5.21 for a pizza. She now has $4.53. With how much money did she start? x - $5.21 = $4.53 x - $5.21 = $4.53

13 Mark ran 28.2 miles less than Cody last week. Mark ran 12.4 miles. How many miles did Cody run? Dan paid $5 for a salad. He now has $ How much money did he have before buying the salad? 3) Write an equation to find the missing angle, and use inverse operations to solve and check.

14 Expressions & Equations: HW #57 4) Solve each equation, and check your solution. 2 3 x = x = = 15q 60 = 15q n 7 = 4 n 7 = 4 t 6 = 12 t 6 = 12 Vincent and some friends shared the cost of a package of blank CDs. The package cost $24 and each person contributed $6. How many people shared the cost of the CDs? Write a multiplication equation with a variable, and then use inverse operations to solve and check.

15 5) The Walkers traveled 182 miles in 3 ½ hours. The equation 3.5m = 182 can be used to find their mean rate of travel. What is the value of m? 4) Hannah is putting in a tile floor. She needs to determine the angles that should be cut in the tiles to fit in the corner. The angle in the corner measures 90. One piece of the tile will have a measure of 38. Write an equation and use it to determine the measure of the unknown angle.

16 Expressions & Equations: HW #58 1) Solving Equations - Use inverse operations to solve and check the following equations. 1 5 n = 85 1 n = = 32 t 128 = 32 t 16g = g = 192

17 2) Jose and nine of his friends went out to eat. They decided to split the bill evenly. Each person paid $ What was the total bill? Write an equation with a variable for the problem below. Then use inverse operations to solve and check. 3) Michelle is designing a parking lot. She has determined that one of the angles should be 115. What is the measure of angle and angle y? Angle x = Angle y =

18 Expressions & Equations: HW #59 Quiz Review Translating & Solving Equations Write an equation with a variable for each of the problems below. Then use inverse operations to solve and check. 1) Amy and four of her friends went out to eat. They decided to split the bill evenly. Each person paid $ What was the total bill? 2) If the weight of a package is multiplied by 5 7 the result is pounds. Find the weight of the package. 3) A stray dog ate 12 of your muffins. That was 3 of all of them! With how many did you start? 10 4) Find the measure of the missing angle.

19 5) In your own words, explain what it means to isolate the variable. Please write your response in complete sentences. 6) Solve each equation, and check your solution. 2 x = 54 2 x = = 42y 546 = 42y n 6 = 14 n 6 = 14 9 = p 12 9 = p 12

20 Expressions & Equations: HW #60 Write an algebraic expression for the following statements. 1) 5 less than the sum of 6 and a number 2) 9 times the quotient of 30 and a number 3) twice a number, multiplied by 7 4) the sum of x and 10, multiplied by 3 5) 10 less than the sum of 19 and a number 6) the quotient of 7 and a number, increased by 8 7) Solve for the variable by using cross products. 8) Solve for the variable by using cross products. 9) Solve for the variable by using cross products. 10) Solve for the variable by using cross products.

21 11) the difference of a number and 8, divided by 5 a) (n/50) + 3 b) (n - 8) / 5 c) 0.30c + 5 d) 8n 10 12) Simplify the following expressions by combining like terms.

22 Expressions & Equations: HW #61 1) the sum of 7 and a number, divided by 7 2) the difference of a number and 8, divided by 5 3) the cost of n sandwiches at $3 each, minus $0.50 4) one-fourth the difference of 12 and a number 5) 3 less than the difference of a number and 7 6) 5 times the product of a number and 20 7) 8) 9) the fraction of n students out of 50, increased by 3 a) (n-3) x 7 b) (n/50) + 3 c) 9 (30/n) d) n 10) 10 dollars plus the cost of 5 sodas at n cents each a) 6 + 2n b) n c) 2n(7) d) 3 ( 24 - n)

23 11) Fill in the number of items on the chart for each question. Then you must set up an equation by combining like terms. 12) Lisa has created a cover for her boat. Her sample design measures 7 yards wide and 14 yards long. If she enlarges the cover to a 10 yard width, what will its new length be?

24 Expressions & Equations: HW #62 1) The rates for renting a car are shown in the table below. Glades Car Rental Cost Per Day $19.00 Cost Per Mile $0.15 Which expression could be used to find the cost of renting a car for 3 days and driving m miles? a) m b) 19m c) m d) 3m + 19(0.15) 2) 23 decreased by the sum of 18 and a number a) (n - 8) / 5 b) 23 - (18 + n) c) (7 + n)/7 d) (n/50) + 3 3) Define a variable and write each phrase as an algebraic expression. The first one has been done for you. 3 more than four times as many apples a = apples 3 + 4a 7 less than ten more shoes than Rob $5 dollars less on dinner than James spent plus $7 tip 3 more than twice as many ringtones as Mary 4) Kiyo bought a pizza for $12.75 and four medium drinks at Pauli s Pizza. Define a variable and write an expression to represent the total amount of money he spent. Then find the total cost if one drink costs $3. Expression: Total Cost:

25 5) Simplify the following expressions by combining like terms. 6) A cookie recipe calls for 8 cups of flour and 4 tablespoons of butter. If Jake makes a smaller batch using only 5 cups of flour, how many tablespoons of butter will he need?

26 Expressions & Equations: HW #63 1) 4 times the sum of 19 and a number 2) 6 dollars plus the cost of n notebooks at 2 dollars each 3) 23 more than a number, increased by 7 4) twice the difference of 18 and a number 5) The number of restaurants on Boland Street is 3 less than 4 times the number of restaurants, r, on Macaw Street. Which expression can be used to determine the number of restaurants on Boland Street? a) 7r b) 12r c) 3-4r d) 4r-3 6) What algebraic expression represents "three times the difference of a number, x, and nine equals 15?" a) 9x - 3 = 15 b) 3(9) - x = 15 c) 9-3x = 15 d) 3(x - 9) = 15 7) Solve for the missing variables below by using cross-products. 70 x x 0.9 x

27 8) Mark the text by underlining key words, and then write an expression using variables and numbers for each of the statements below. a) A number h is tripled and then decreased by 8. b) The square of p reduced by 34. c) The quotient when the quantity of 48 plus p is divided by 6. d) 12 less than the quantity of 7 times n. 9) Simplify the following expressions by combining like terms.

28 Expressions & Equations: HW #64 Write an inequality for each sentence. 1. You must be older than 13 to play in the basketball league. 2. To use one stamp, your domestic letter must weigh less than 3.5 ounces. 3. You must be over 48 inches tall to ride the roller coaster. 4. You must be at least 18 years old to vote. 5. You cannot spend more than $ More than 800 fans attended the opening soccer game. 7. Swim practice will be no more than 35 laps. 8. Kevin ran for less than 5 miles. 9. Suppose a DVD costs $19 and a CD costs $14. Write an inequality to find how many CDs you can buy along with one DVD if you have $65 to spend. 10. There are dogs and cats in a kennel. The number of cats is twice the number of dogs. What is the greatest number of cats in the kennel if there are at most a total of 48 animals in the kennel? Translate the statement into inequality form using the clues.

29 Expressions & Equations: HW # Fill in the information that is missing in the chart. The first one is done for you. Symbol Words Open or closed dot on the number line? > greater than open dot greater than or equal to less than 2. Choose the number(s) that make the equation or inequality true from the following set of numbers: {0, 1, 5, 8, 11, 17} Write none, if no there is no value in the given set will make the inequality true. m+5=6 m+5 6 5h=40 5h> y=5 k 3=20 3. Graph the inequalities on the number lines provided, or write the inequality represented by the graph. 4. Write an inequality to represent each situation. Then graph the solution. a) The town of Blayton is at most 2 meters above sea level. b) Edith must read for a minimum of 20 minutes.

30 Expressions & Equations: HW # Solve and graph the following inequalities. 5x 45 5x 45 X + 8 > 10 X + 8 > Translate each verabl phrase into an algebraic expression.

31 3. Choose the correct inequality that best describes each graph. 4. Circle the possible values that satisfy each inequality. 5. Choose the correct graph that best describes the solution for each inequality. 6. Solve each inequality and graph the solution.

32 Expressions & Equations: HW #67 1. Choose the correct inequality that best describes each graph. 2. Solve each inequality and graph the solution. Use the T-Charts to help solve and check your work.

33 3. Circle the possible values that satisfy each inequality. 4. Translate each verabl phrase into an algebraic expression. 5. Choose the correct graph that best describes the solution for the inequality below.

34 Expressions & Equations: HW # 68 Quiz Review Write an inequality for each sentence # The movie will be no more than 90 minutes in length. 2. The mountain is at least 985 feet tall. 3. The heavyweight division is greater than 200 pounds. 4. Which of the following numbers make the equation and/or inequality below true? {0,3,5,8,10,14} m+4=12 f 4<2 1 2 h 4 5. Write an expression using letters and numbers for each problem below. 4 less than the quantity of 8 times n. The square of m reduced by times the sum of y and 11. The quotient when the quantity of 17 plus p is divided by Solve and graph the following inequalities. 7x > 56 7x > 56 d 3 2 d 3 2

35 7. Tino s pizza charges $9 for a cheese pizza. Eileen has $45 to buy pizza for the Spanish club. Write, solve, and graph an inequality to find the maximum number of pizzas that Eileen can buy. 8. Solve the following problems using cross-products and circle the correct answer. Ken earned $ for 25 hours of work. At the same rate, how much would he earn for 40 hours of work? a) $ b) $ c) $ d) $ $ hours = x 40 hours 9. Choose the correct inequality that best describes each graph. 10. Choose the correct graph that best describes the solution for each inequality.

36 Expressions & Equations: HW #69 1. A car travels at a constant rate of 60 miles per hour. a) Complete the table below. Time (h) Distance (mi) b) What is the independent variable, and what is the dependent? 2. For each table below, write an equation that expresses y in terms of x. The first one has been done for you. x y x y x y y = x Sarah is purchasing pencils to share. Each package has 12 pencils. The equation n=12p, where n is the number of pencils and p is the number of packages can be used to determine the total number of pencils Sarah purchased. Determine which variable is dependent and which is independent. Then make a table showing the number of pencils purchased for 3 7 packages. # of packages total # of pencils Independent Variable: Dependent Variable: Equation:

37 4. Charlotte reads 4 books each week. Let b be the number of books she reads each week and let w be the number of weeks that she reads. Determine which variable is dependent and which is independent. Then write an equation to model the situation, complete the table, and make a graph that shows the number of books read in under 6 weeks. # of weeks # of books Independent Variable: Dependent Variable: Equation: 5. Stewart is playing a video game. He earns the same number of points for each prize he captures. He earned 1,200 points for 6 prizes, 2,000 points for 10 prizes, and 2,600 points for 13 prizes. Which is the dependent variable in the situation? a) the number of prizes captured b) the number of points earned c) the number of hours d) the number of prizes available.

38 Expressions & Equations: HW #70 a. A miniature golf course has a special group rate. You can pay $20 plus $3 per person when you have a group of 5 or more friends. Let f be the number of friends and c be the total cost. Determine which variable is independent and which is dependent, and write an equation that models the situation. Then make a table to show the cost for 5 to 12 friends. # of friends f total cost c Independent Variable: Dependent Variable: Equation: b. Carlos is shopping for school supplies. He bought a pencil box for $3 and he also needs to buy notebooks. Each notebook is $2. Let t = the total cost of the supplies and n be the number of notebooks. Determine which variable is independent and which is dependent, and write an equation that models the situation. Then make a table to show the cost for 1 to 5 notebooks. # of notebooks n total cost t Independent Variable: Dependent Variable: Equation:

39 c. Xin is buying beverages for a party, which are individually packaged and come in packs of 8. Let p be the number of packages Xin buys and t be the total number of beverages. The equation t=8p can be used to calculate the total number of beverages when the number of packages is known. Determine the independent and dependent variable in this scenario. Then make a table using whole number values of p less than 6. # of packages (p) Total Number of Beverages (t=8p) Make a graph for the table above. Be sure to include all necessary labels.

40 Expressions & Equations: HW #71 Unit Exam Review 1. What is the value of s in the equation below? Show all your work & check! 7s = 91 7s = What is the value of the expression h 3 + m 2 when h = 4 and m = 8? 3. Write an equation that represents ten less than a number plus sixteen equals eighteen. 4. What is the value of x in the proportion below? 10 x =

41 5. Write an inequality for the following statement. 6 times a number plus 4 is greater than Joshua had $860. He has $280 left after paying his rent. Write an equation that can be used to find r, the amount of Joshua s rent. 7. Anna started with $10. She saved an additional $5 each week. Write an equation that can be used to determine the total amount saved, t, after a given number of weeks, w. Determine which variable is independent and which is dependent. Then graph the total amount saved for first 5 weeks. Independent Variable: Dependent Variable: Equation:

42 8. Thomas is putting in a tile floor. He needs to determine the angles that should be cut in the tiles to fit in the corner. The angle in the corner measures 90. One piece of the tile will have a measure of 24. Write an equation and use it to determine the measure of the unknown angle. 9. Write an inequality to represent the situation below. Then graph the solution. a) A gym charges $4 per hour to swim in the pool. If a member only has $24 to spend each month on swimming, at most how many hours can the member swim? 10. What is the value of the expression below? 18 + (12 3 ) 2 3

43 Expressions & Equations: HW #72 Unit Exam Review 1. A fisherman catches an average of 20.5 fish each month. If the fisherman catches the fish for a certain number of months, m, write an expression to determine the total number of fish caught? 2. Which expression is equivalent to 8(6 + y)? a) 48y b) 48 + p c) y d) 14y 3. What is the value of this expression when t = 3 and r = 15? 90 (10 x t) + r 4. Your younger sister asks you for help to do the following problem: Evaluate the expression 6 + (n 2) 3 + n 2 for n = 5 5. Simplify the expression below by combining like terms. 8y + 5x 3y + 7 2x

44 6. Evaluate each of the expressions below when x = 3 and y = 4. a. 6x + 21y b. 3(2x + 7y) 7. Find the value of h in the equation below. 96 h = h = A chef mixes 6 gallons of water with 4 gallons of juice. How many gallons of water does the chef need to mix with 24 gallons of juice? 9. Write an inequality to represent the situation below. Then graph the solution. a. Kelly works for Quick Oil Change. If customers have to wait longer than 20 minutes for the oil change the company does not charge for the service. The fastest oil change that Kelly has ever done took 6 minutes. Show the possible customer wait times in which the company charges the customer.

45 10. <BAE measures 90. Solve for x. 11. Write an algebraic expression for the following statements. a. a raised to the fifth power then increased by the product of 5 and c. b. The quantity of a plus b divided by 4. c. 10 less than the product of 15 and c.

46 Expressions & Equations: HW #73 Unit Exam Review 1. Nick s car gets 32 miles per gallon. How many miles can he go on 6 gallons? 8 gallons? 10 gallons? a. Identify the independent and dependent variables. Independent variable Dependent variable b. Make a table for the problem. c. Write an equation for the problem. 2. Write an algebraic expression or equation for the following statements. a. the difference of v and 21 is 80 b. the product of 14 and u

47 c. twenty-six added to the product of twenty-eight and z 3. The number of restaurants on Boland Street is 3 less than 4 times the number of restaurants, r, on Macaw Street. Which expression can be used to determine the number of restaurants on Boland Street? a. 7r b. 12r c. 3-4r d. 4r-3 4. What algebraic expression represents "three times the difference of a number, x, and nine equals 15?" a. 9x - 3 = 15 b. 3(9) - x = 15 c. 9-3x = 15 d. 3(x - 9) = Solve for the missing angle. 6. What is the value of x in the equation below? Show all your work & check! 14x = x = 154

48 7. What is the value of the expression x 3 + y 2 when x = 12 and y = 5? 8. Solve the inequality and graph the solution. Use the T-Chart to organize your work. 9. Simplify each expression. 10. Write an inequality to express the number line. 11. Simplify the expression below using the Order of Operations (PEMDAS).

49 Expressions & Equations: HW #74 Unit Exam Review 1. Diane makes $9.00 for every lawn she mows. How much money will she make if she mows between 5 and 10 lawns? a. Identify the independent and dependent variables. Independent variable Dependent variable b. Make a table for the problem. c. Make a graph for the problem. d. Write an equation for the problem. 2. Simplify the expression below using the Order of Operations (PEMDAS).

50 3. Determine the measure of the missing angles ABD and DBC. ABD DBC 4. Use the numberlines provided to graph each inequality below. 5. A scientist mixes 20 ounces of water with 12 ounces of vinegar. How many ounces of water would he need to mix with 24 ounces of vinegar to maintain the same proportion? water vinegar = water vinegar 6. Lisa wants to buy a pair of boots and socks. The boots costs $45. She does not want to spend more than $50 for both the boots and socks (excluding tax). Write an inequality that represents s, the amount that Lisa can spend on the socks? 7. Write and inequality for the following statements. Hint: Remember to write the variable first.

51 8. Using the variable x, write an equation to represent the statement below. 8 more than 6 times a number is 74 Equation: 9. Solve the inequality below, then graph it. 24y Simplify the expression below. 11. Simplify the expression below using the Order of Operations (PEMDAS). 7 + ( )