UNIT #2 LINEAR EXPRESSIONS, EQUATIONS, AND INEQUALITIES REVIEW QUESTIONS
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1 Name: Date: Part I Questions UNIT # LINEAR EXPRESSIONS, EQUATIONS, AND INEQUALITIES REVIEW QUESTIONS 1. The value 4 is a solution to all of the following equations ecept which? 1. () (1) (3) (4) 1 5. Which of the following is the solution to 3 10?. 5 (1) 47 () 1 (3) 35 (4) 5 3. The sum of a number, n, and a number 5 larger than it is 41. Which of the following 3. equations could be used to solve for the number? (1) n5n 41 () n n 5 41 (3) 5 n 1 41 (4) 5n n Which of the following is not an equation? () 4 1 (3) (4) 1 7 (1) 5. Which of the following values of solves ? 5. (1) 1 () 0 (3) 8 (4) 6 6. The inequality 1 15 will be true when 6. (1) 7 () 0 (3) 10 (4) 5 7. If the epression b c is solved for in terms of a, b, and c, then 7. a (1) ac ab (3) ac b () b c a (4) ab c COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT #
2 8. Which of the following compound inequalities is shown graphed below? (1) 1 5 () 1 5 (3) 1 or 5 (4) 1 or 5 9. The sum of two consecutive odd integers is at least 16. Which of the following 9. inequalities would model this statement? (1) n n3 16 (3) n n 16 () n n 16 (4) n n Jenna manipulated the equation by adding 7 to both sides. Which of the following properties justifies this manipulation? 10. (1) The associative property of addition. () The addition property of equality. (3) The commutative property of addition. (4) The multiplication property of equality. 11. Jody's older brother is only three years less than twice Jody's age. If the sum of their ages 11. is 30, then which of the following is the age of Jody's brother? (1) 7 () 11 (3) 19 (4) 3 1. The solution to 7 15 is the set 1. 3 (1) 1 () 6 (3) 33 (4) Which of the following intervals is equivalent to the statement 3 9? 13. (1) 3, 9 (3) 3, 9 () 3, 9 (4) 3, Which of the following compound inequalities is not true? 14. (1) 5 3 and (3) 5 or 6 10 () 6 1 and 6 1 (4) 4 or 3 1 COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT #
3 Free Response Questions 15. A rectangular garden has a length that is si feet more than twice its width. It takes 10 feet of fencing to completely enclose the garden's area. Write an equation that could be used to find the width of the garden. Clearly define your variable. Eplain how your equation models the given information. Find the length of the garden algebraically. Show how you arrived at your answer. 16. Two consecutive even integers have the following property. When the smaller integer is added to three times the larger integer, the result is two less than five times the smaller integer. Rafael tries to model this scenario with the equation show below. Unfortunately, Rafael has made an error on the left side of the equation. Eplain what error he made. n 3n 5n Write the correct equation (if you haven't already) and solve it to find the two consecutive even integers. 17. Solve the following equation for v in terms of all other variables involved. v h k r COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT #
4 18. Give a property of real numbers (associative, commutative, or distributive) or a property of equality (addition or multiplication) that justifies each step in the solution of the equation shown below (1) (1) () () (3) (4) (3) (4) (5) (5) (6) (7) (6) (7) 19. Water is being drained out of a swimming pool at a constant rate of 780 gallons per hour. The swimming pool initially contained 45,000 gallons of water. A chemical additive must be added to the pool when it has no more than 15,000 gallons of water remaining in the pool. Write an epression for the amount of water remaining in the pool after h-hours. Write an equation that could be solved to find the least number of hours before the chemical could be added. Will it take longer than two days before the chemical can be added? Justify your response. COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT #
5 0. The trapezoid below has legs with lengths y feet and one base that is four feet longer than the other base,. The perimeter of this trapezoid is given by P y 4. Solve this equation for the leg length, y. 4 y y If the perimeter of the figure is 6 feet and the shorter base,, is 8 feet, then find the length of the leg, y. 1. Consider the inequality: Rewrite this as two inequalities. Should they be joined with OR or AND? Is 3 part of the solution set of this compound inequality? Justify your response. Solve the inequality and graph its solution set on the number line below. COMMON CORE ALGEBRA I, UNIT REVIEWS UNIT #
UNIT #2 LINEAR EXPRESSIONS, EQUATIONS, AND INEQUALITIES REVIEW QUESTIONS
Name: Date: Part I Questions UNIT # LINEAR EXPRESSIONS, EQUATIONS, AND INEQUALITIES REVIEW QUESTIONS 1. The value = 4 is a solution to all of the following equations ecept which? 1. (1) + 7 = 15 () 3 +
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