6 th Math Common Assessment Unit #3B PART ONE: Expressions and Equations Form A (6.9A, 6.9B, 6.9C, 6.10A, 6.10B)

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1 6 th Math Common Assessment Unit #3B PART ONE: Expressions and Equations Form A (6.9A, 6.9B, 6.9C, 6.10A, 6.10B) Name: 1. (6.9A) Eric is trying to earn enough money to rent a house on the beach for the week. After much research, he finds that the house will cost more than $1,340 for the week. Eric already has $850 in his savings account. Which inequality represents m, how much more money Eric must raise to go to the beach house? A. 850 < m B < m C < m 850 D. 850 < m 1340 When buying something, the money that you have plus what you still need to earn must be more than the cost of what you want to purchase. For the inequality above, choose the one that shows the sum of the amount Eric has, added to m, what he still needs to earn, is more than the cost of renting the house. 2. (6.9B) Decide which statement(s) are true for the graph. I. The graph shows the solution of 2x 8. II. The graph shows the solution of 24 3x. III. The graph shows the solution of both x 3 5 and x A. I only B. I and II C. III only D. II and III For each inequality in I, II, and III, you must substitute one or more values from the solution set shown by the number line for x and simplify the statement. For example: I. 2x 8 Substitute 8 for x. 2(8) 8 Is 2 x 8 less-than-or-equal-to 8? II. 24 3x Substitute 6 for x 24 3(6) Is 24 greater-than-or-equal-to 3 x 6? Substitute more than one value for each statement to be sure. Then choose which statement(s) are correct.

2 3. (6.9B) Misty wants to buy a new phone that costs $399. She has $149. Which solution best represents the amount of money Misty still needs to purchase the phone? A. B. C. D. Subtract the amount that Misty has from the cost of the phone. Then choose the graph that shows this amount. 4. (6.9C) Which situation below is best represented by the equation 3x = 27? A. The total cost of a dinner including tip was $27. If a $3 tip was included in the total cost, what is x, the cost of the dinner? B. The total cost of a dinner and dessert was $27. The cost of the dinner was 3 times the cost of the dessert. What is x, the cost of the dessert? C. Three friends went to dinner, and each paid $27. What is x, the total amount they spent on dinner? D. Three friends went to dinner and paid a total of $27. If they divided the bill evenly, what is x, the amount each friend paid? The equation shows that 3 times some number equals 27. You must reason each situation out to find the best fit. A. The total is 27. To find the cost of the dinner you must subtract the $3 tip that is included in the total. B. The total is 27. If the dinner is 3 times the cost of the dessert, then the dinner is 3x and the dessert is 1x. That s 4x. C. If each friend paid $27, then the total cost is 3 times $27. D. The total is 27. If x is the amount that each friend paid, then the total cost is 3 times x, or 3x.

3 5. (6.9C) Which situation below is best represented by the inequality 32 + h 36? A. You must be 36 inches to ride the Super Slide at the water park. Mason is 32 inches tall. What is h the number of inches Mason needs to grow to ride the Super Slide? B. You must be at least 36 inches to ride the Super Slide at the water park. Mason is 32 inches tall. What is h the number of inches Mason needs to grow to ride the Super Slide? C. You must be shorter than 36 inches to ride the Super Slide at the water park. Mason is 32 inches tall. What is h the number of inches Mason can grow and still ride the Super Slide? D. You must be taller than 36 inches to ride the Super Slide. Mason is 32 inches tall. What is h the number of inches Mason needs to grow to ride the Super Slide? Look at the clue words that compare 36 inches in each situation. A. The words must be 36 inches indicate an exact amount, so you must equal (=) 36 inches to ride. B. The words must be at least 36 inches indicate an amount equal to or greater than ( ) 36 inches to ride. C. The words must be shorter than 36 inches indicate an amount less than (<) 36 inches to ride. D. The words must be taller than 36 inches indicate an amount greater than (>) 36 inches to ride. 6. (6.10A) The model below represents x 5 = 2. What is the value of x? A. 3 B. 5 C. 7 D. 2 x = Since 5 is subtracted from x, simplify the equation by adding 5 to both sides of the equal sign. x 5 = 2 x = Complete the equation to find the value of x.

4 7. (6.10A) The model below represents the equation 3x = 5. What process would you use to find the value of x? A. Subtract 3 from each side of the model. B. Add 5 to each side of the model. C. Divide each side of the model into 3 groups. D. Divide each side of the model into -5 groups. Look at the equation. It is more helpful than the model illustration. To isolate the variable (get the x all by itself), you should do the opposite of multiplying 3 by x. 8. (6.10A) Hector bought several pieces of gum for $3.00. If the gum costs 15 cents each, the equation 0.15x = 3 can be used to find x, the number of pieces Hector bought. How many pieces of gum, x, did Hector buy? A pieces because you multiply both sides by 0.15 B. 2 pieces because you divide both sides by 15 C. 5 pieces because you divide both sides by 3 D. 20 pieces because you divide both sides by 0.15 Look at the equation. To isolate the variable (get the x all by itself), you should do the opposite of multiplying 0.15 by x. The opposite of multiply is divide. Divide both sides by the number that multiplies x (the coefficient). 9. Nikki bought a PS4 game for $ She saved $7.53 by trading in three older games. She used the following equation to find p, the original price of the game. What is the original price, p, of the game? A. $21.94 p = B. $24.94 C. $40.00 D. $43.00 Since 7.53 is subtracted from p, simplify the equation by adding 7.53 to both sides of the equal sign. p = p = Complete the equation to find the value of x.

5 10. The graph below shows possible solutions to the inequality, x > 4. Which of the following values of x would make this not true? A. x = 4 B. x = 4 C. x = 2 D. x = 5 Since negative x is greater than negative 4, then positive x is greater than positive 4 (divide both sides by -1). Any number can t be greater than itself, so that number would make the inequality not true.