Study Guide Unit 4 Test “equations and inequalities” Name:_________________________________________________________________________________ Date: _____/_____/__________ Study Guide Unit 4 Test “equations and inequalities” 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/ inequalities” TEST: Modeling One -Step Equations (Balance scale with algebra tiles) Solving One and Two-Step Equations Equation Word Problems Solving One-Step Inequalities Graphing One-Step Inequalities NOTES SPACE/HELPFUL TIPS (to be filled out in class):

Modeling equations One-Step Equations: Draw tiles onto the below balance scales in order to model the following: One-Step Equations: 1. x + -2 = 3 2. 5 + x = -1 3. x + (-6) = 2 4. x – 7 = -1 x – (-3) = 6 6. x – (-2) = -3 Two-Step Equations: 7. 2x + 4 = -8 8. 3x + (-1) = 14

One-step equations Solve the following addition/ subtraction one-step equations: 1) x + 3 = -21 2) 4 + x = 16 x – 2 = -1 4) x – (-4) = -30 5) -12 + x = 28 6) x – (-100) = 75 7) x + 9 = -5 8) -15 = -6 + x 9) -4 = x – 24 Solve the following multiplication/ division one-step equations: 1) 3x = -21 𝒙 𝟒 = -8 -8x = 64 4) 99 = 9x 5) 𝒙 −𝟔 = -7 6) 𝟑 𝟒 x = 6 7) 3x = -21 8) 𝟐 𝟓 x = -4 9) 64 = -8x

two-step equations Solve the following two -step equations: 1) 5x + 4 = -21 x + 2 = -8 4 -8x – 2 = 62 4) 1 + 9x = 73 5) x – 8 = -2 -6 6) 3 x + 3 = 6 7) 15 = 3x + 12 8) 2 x - 3 = 5 5 9) 9 - 7x = 58 10) 18 = 4x + 6 11) x - 3 = 6 11 12) 3 - 12x = 51

equation word problems SITUATION EQUATION ANSWER Last week Frank ran 4 more miles than his dad. Frank ran 16 miles. How many miles did his dad run? What is the maximum amount of pop rocks packages you can buy with $4.00 if one package costs $0.80? You would like to save $200 for vacation spending money. You already have $30 in your savings account and you plan on saving $10 per week. How many weeks will it take you to save the money? You purchase three school play tickets, plus some concession goodies for $7. If you spent a total of $25, how much was each ticket? You sold five times the amount of girl scout cookie boxes that Sheila sold. If you sold 80 boxes, how many did Sheila sell? Mrs. Dyson unpacks a box of Christmas ornaments. She splits the ornaments equally among herself and her three family members. Then, she finds an additional 2 ornaments that she keeps for herself. If Mrs. Dyson ends up with a total of 24 ornaments (counting the extra two), how many ornaments were in the original box? 344 seventh- graders went on a field trip to Washington D.C. 15 students traveled by car and the rest were equally split among 7 school busses. How many students were on each bus?

solving and graphing inequalities Fill-in-the-Blanks: When multiplying or ______________________________ by a negative number, we __________________________ the inequality sign!!! For the following inequalities, decide whether you would need to switch the direction of the sign. Write “yes” or “no” in the blanks: 2) __________ x + -3 > 4 3) __________ 2x ≤ -4 4) __________ x > 4 -4 5) __________ -5x < 20 6) __________ 32 – x ≥ 4 7) __________ x ≤ 4 9 Solve each inequality and circle ALL the numbers that makes the inequality true: 8) x + 5 > -2 9) -3x ≤ 33 10) x – 7 < -2 11) x ≥ 20 -4 -6 -8 -7 7 -9 -11 -12 -9.5 11 12 -1 6 7 -9 5 4 2 -90 -5 -4 -81 -80.5 -80 Solve AND graph the following inequalities: 12) x + 9 > 2 12) -5 + x < 2 12) -6x ≥ 30 25 > 5x 12) x ≤ 4 - 2 12) 15 + x < 24 12) x > 3 3 12) -12x < 60 12) x + -45 ≥ -47

multiple choice 1. Apples cost $0.55 each, and oranges cost $0.75 each. Edward bought 8 apples, and some oranges. If he spent a total of $8.15, how many oranges did Edward buy? (pick correct equation) Casey earns $24 a day, plus $8 for each doll she assembles. Yesterday she earned $104. How many dolls did Casey assemble? (Pick the equation that correctly represents this situation) 3. Which of the following equations represents the given model? x + 5 = 40 5x = 40 x – 5 = 40 𝐱 𝟓 = 40 Rick paid $40 down on a stereo system and then made equal payments until he paid it off. He paid $240 in all. What more do you need to know to find how much he paid each month? A. What kind of music Rick likes. The amount of time it took to find the stereo. The number of payments he made. How much $ he makes at his job. 5) What is the value of “x”? x = 4 x = 6 x = 8 x = 10 6) Kira had 3 baskets of strawberries. Each basket contained the same number of strawberries. After giving 10 strawberries to her friend, she had 26 strawberries left. How many strawberries were in each basket? 3 10 12 36

9. Two-thirds less than 5 times a number is 44. Which equation represents this statement? 10. Tara bought three DVDs at the same price and paid $4.07 in sales tax. She spent $54.92 in all. How much did each CD cost? 11. Which of following numbers is A solution to the inequality? 5x > 45 A 8 B 9 C 10 D 7 12. What is the solution to the inequality? -6v < 144 13. Which inequality has the following solution? A 8 + x > 16 B x – 8 > 11 C 8x < 24 D x + (-5) > -2 14. a solution to the inequality? -2x > 40 A -20 B -19 C -21 D 20