Study Guide “Equations Test”

1. Study Guide “Equations Test” Name: Date: Note: Many problems in this packet will be completed together in class during review time. Students are not expected to complete every single problem in the packet. They should complete several problems from each page-- in addition to studying the notes and past quizzes– in order to be fully prepared for test. TOPICS COVERED ON “Equations” TEST: Math Properties One and Two Step Equations Distributive Property Equations Combining Like Terms Equations Equations with Variables on Both Sides NOTES SPACE/HELPFUL TIPS (to be filled out in class):

2. Properties Identify the properties used for EACH STEP in order to simplify the following expressionsor equations: 1. 8 + 5 + (-8) Step 1 = 8 + (-8) + 5 _____________________________ Property of Addition Step 2 = [ 8 + (-8) ] + 5 _____________________________ Property of Addition Step 3 = 0 + 5 _____________________________ Property of Addition Step 4 = 5 _____________________________ Property of Addition 2. 7+ [3(3 + 11)] + 1 Step 1 = 7 + [9 + 33] + 1 _____________________________ Property Step 2 = 1 + [9 + 33] + 7 _____________________________ Property of Addition Step 3 = [ 1 + 9] + [ 33 + 7] _____________________________ Property of Addition Step 4 = 10 + 40 Step 5 = 50 3. [(3/4 )(25) (4/3) ] + (-25) Step 1 = [ (3/4)(4/3)(25) ] + (-25) _____________________________ Property of Mult. Step 2 = [ 1(25)] + (-25) _____________________________ Property of Mult. Step 3 = [ 25] + (-25) _____________________________ Property of Mult. Step 4 = 0 _____________________________ Property of Add. 4. x(7 + 8) + ( -5 + 5) = Step 1 7x + 8x + (-5 + 5)= 60 __________________________ Property Step 2 7x + 8x + 0 =60 __________________________ Property of Addition Step 3 (7x + 8x) + 0= 60 __________________________ Property of Addition Step 4 15x = 60 Step 5 (1/15)15x = 60(1/15) __________________________ Property of Mult. Step 6 x = 4 5. 3y + 6 – 7y - 2 =16 Step 1 3y – 7y + 6 - 2 = 16 _________________________ Property of Addition Step 2 (3y – 7y) + (6 – 2) =16 ________________________ Property of Addition Step 3 -4y + 4 = 16 Step 4 -4 -4 _________________________Property of Addition Step 5 -4y = 12 Step 6 ( -1/4) -4y = 12 (-1/4) _______________________ Property of Mult. Step 7 y = -3

3. One and Two Step Equations

4. Distributive Property Equations

5. Combining Like Terms Equations

6. Equations with Variables On Both Sides

7. Word Problems • Write an equation and solve: • 1) A large trash can containing 5 tires weighs 13.9 Kg. The trash can, when empty, weighs 2.2 Kg. How much does one tire weigh? Let “t” represent the weight of one tire. • 2) Barry purchases 8 computers for the same price, and a printer for an additional $85. If the total bill was $7,919 how much did one computer cost? Let “c” represent the cost of one computer. • 3) A basket full of buttons weighs 2.1 Kg. The basket, when empty, weighs 0.24 Kg. If there are 80 buttons in the basket, how much does one button weigh? • 4) Jerry buys 5 baseball bats for the same price, and a batting helmet for $11.50. If the total bill was $75.95, how much did he pay for one baseball bat? • 5) Jed buys calculators for his entire class of 25 students. He also buys a yard stick for $8.95. If the total bill was $320.20, how much did each calculator cost? Let “c” represent the cost of onecalculator. • 6) A bin of 20 playground balls weighs 153 pounds. The bin, when empty, weighs just 4.8 pounds. How much does each ball weigh? Let “b” represent the weight of one playground ball. • 7) Kip buys 8 bouquets of flowers (for the same price) and a shovel for $14.65. If his total bill was $186.65, how much was each bouquet of flowers? • 8) A storage crate containing 14 bicycles weighs 600 pounds. The storage crate, when empty, weighs 47 pounds. How much does each bicycle weigh (assuming they each weigh the same)?

8. Multiple Choice • 6) Solve for p: 15 + 7p = 2p • A p = 5 • B p = 3 • C p = -3 • D p = -5 • 7) What value of c makes this equation true? 5c – 3 = 2c + 6 • A c = 3 • B c = 9 • C c = -3 • D c = 1 • 8) A crate containing 4 boxes of gummy worms weighs 8.4 Kg. The crate, when empty, weighs 5.2 Kg. Use “g” to represent the weight of one box. • A 4(g + 8.4) = 5.2 • B 4g + 5.2 = 8.4 • C 4g = 8.4 • D 5.2 + 8.4 = 4g • 9) Lilly buys a few cassette tapes from the clearance bin marked “$2.50 each”. She also buys a brand new CD for $15.99. Her total was $43.49. Use “c” to represent the number of cassette tapes. • A 15.99 + 2.50 = 43.49 • B 2.50c + 15.99 = 43.49 • C 15.99c – 43.49 = 2.50 • D 2.50c = 43.49 • What property is used to justify this step? • 3(x -5) = 14 • 3x – 15 = 14 • A Associative Property • B Identity Property • C Commutative Property • D Distributive Property Billy purchases 4 value meals for $14.80. Included in that total was the $0.84 in sales tax. Use “v” to represent the cost of one value meal. A 4v + 0.84 = 14.80 B 4v – 0.84 = 14.80 C 14.80 + 0.84 = 4v D 4 + 0.84 = 14.80v A salesman sold 6 cars in a week and received a check for $2,650. Included in that check is $400 that he gets even if he doesn’t sell a single car. Use “c” to represent how much he gets paid to sell one car (assume he gets paid the same for each one). A 400 – 6c = 2650 B 6c + 400 = 2650 C 400 + 6 = 2650c D c = 2650 3) Solve for g: 1/3 g – 6 = 4 A g = 2 B g = 6 C g = 10 D g = 30 4) Which property would you use to justify this step? 10 + (3x + 5) = 27 10 + (5 + 3x) = 27 A Inverse Property B Identity Property C Associative Property D Commutative Property 5) What is the value of m in this equation? 10 m – 20 = 36 A m = 3 3/5 B m = 4 C m = 5 3/5 D m = 28