OML Sample Problems Meet 4 EVENT 5: Algebra I Linear Inequalities
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1 Meet 4 EVENT 5: Algebra I Linear Inequalities OML Sample Problems 2017 Include: (1) Linear inequalities as long as the inequality is linear in the variable 2 being solved for (i.e. Solve for x : b a x > c ) (2) Explicit instructions for the form of the desired answer: (a) Solve for x (b) State answer in the form { x : } (c) State answer in the form { x } utilizing and or or as necessary to state answer as one solution set (3) Word problems Exclude: (1) Absolute value problems (2) Variables in the denominator Sample Problems: A. Solve for x : 4 x x 3 3 x + > 2 x Answer: x > 3 B. Find the solution set for 2r 1 2r + 8 2r + 4 Answer: or { } C. Find the solution set. State your answer in the form { c : } { c :4c + 4 c + 10 } { c :3c 3 2c 9} Answer: { c : c 6}
2 Name Score School Event 5: ALGEBRA I Linear Inequalities January x A. Solve for x: 2( 3x + 7) 5x > 3 (2 pts) ANSWER: B. Each side of square ABCD is k cm long. Side AB is extended 10 cm through B to form (3 pts) side AE of a rectangle. Side AD is extended 6 cm through D to form side AG of the same rectangle. If the perimeter of the rectangle is at least twice the perimeter of the square, what is the maximum length of AB? ANSWER: cm C. Solve for x: [ 2 + 3x < 3 or 3(x 1) < 2(x 2) ] and 3 < 4x 3 < 7 (5 pts) ANSWER:
3 Name Score School Event 5: ALGEBRA I Linear Inequalities NOTE: In any answer containing an inequality, only the verbal connectives ("and"/"or") may be used. January 2017 A. Solve for x: 2x 3 < x + 5 < 3x + 7 (2 pts) ANSWER: B. Solve for x: 18 < 9x < 6x +10 or x < 5 3x (3 pts) ANSWER: C. Given: 2x 3 < 3x + 32a (5 pts) If 5 < a 10 and x is an integer, find the minimum value of x. ANSWER:
4 Name Score School Event 5: ALGEBRA I Linear Inequalities NOTE: In your answer only the verbal connectives ("and"/"or") may be used. January 2016 A. Solve for x: 23 5x 6( 8 2x) 19 (2 pts) ANSWER: B. Solve for x: 1 > x +1 > 3 and 7 > 2x + 3 > 1 (3 pts) ANSWER: C. Solve for y: 1 ( 2 2 5y) < 6 y or y > 7 1 ( 4 y + 8) (5 pts) ANSWER:
5 Name Score School Event 5: ALGEBRA I Linear Inequalities January 2015 A. Ryan has scores of 80, 85, 97, and 89 on his last four Algebra tests. In what range should (2 pts) his next test score fall in order for him to average a B? (The range of B is 80 to 89, inclusive.) ANSWER: B. Solve for x: 6 < 4 3x < (3 pts) ANSWER: C. Solve for x: 1 x < 3x + 2 and 4 x 1 2 (5 pts) ( ) +1 3( x +1) 1+ 2x ANSWER:
6 Name Score School Event 5: ALGEBRA I Linear Inequalities January 2014 A. 3a + b 11 and 5a + 3b 9. What is the minimum value of 2a + b? (2 pts) ANSWER: B. Find all values of m for which m 6 x 4 (3 pts) values of m as an inequality. ( ) < m 6 x 3 has no solution for x. Express all such ANSWER: C. Keola is shopping for single use cameras. Daylight cameras cost $2.75 and flash cameras (5 pts) cost $4.25. He must buy exactly 20 cameras and wants to spend between $65 and $75. What is the greatest and the least number of daylight cameras he should buy? ANSWER: _greatest: least:
7 Name Score School Event 5: ALGEBRA I Linear Inequalities January 2013 A. Joe's Pie Bakery needs $10 per day to run the ovens. It costs $4 to bake each pie. If $421 is (2 pts) allotted to spend on production each day, what is the maximum number of pies Joe's Bakery can expect to bake each day? ANSWER: pies B. The sum of two integers is less than 102. One integer is four less than three times the other. (3 pts) What are the largest possible values of the two integers? ANSWER: C. Solve for x: x 16x x + 20 and 30x + 47 < 18x + 49 (5 pts) ANSWER:
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26 Meet 4, Event 5: ALGEBRA I Linear Inequalities 2018 A. x < 11 5 B. 8 C. 0< x < A. 1< x < 8 B. x < 10 3 C A. x 6 7 B. 2< x < 0 C. y > A. 49 Ryan s score 94 B. 8 9< x < 16 3 C. x A. 5 B. m 9 2 C. greatest: 13, least: A. 102 pies B. 74 and 26 C. 3 4 x < A. x 3 B. 18, 79 C. 23< x < A. $10 B. C. 17 x 7 2 or 5< x < A. x < 3 2 B. 0< w 10 C. 5 miles 2009 A. 53 to 93 B. { x : x 3} C. 9g < v < 12g 2008 A. { x : x < 9 2} B. x > 4 3 C. 28 and A. 92, 53 B. 2 x < 7 4 C. 0, 1, 2, 3, A. x B. x 67 C. x > A. x 5 B. 2 x 3 C. 23< x < A. x 1 B. 4 x 3 C. 1< x < A. x 313 B. x 15 C A. x < 16 3 B. 4 7< x 1 9 C. 3 x A. x B. x 2 C. 3 Note: Answers are shown as they appear on the original answer keys. There may be inconsistencies with the formatting of these answers. In all cases, consult the Guidelines for Forms of Answers to determine the correct formatting.
27 2000 A. y 68 9 B. { z : z > 2 3} C A. 10 < x 5 B. 2a+ 3b x > 5 C. 0< w < A. x < 1 or x > B. x 2 C. At least 4 quarts 1997 A. x > 25 3 B. x > 32 C. x < 2a+ b 1996 A. x 38 B. x 1 C. x > A. 12< x 0 B. a C. 14 Note: Answers are shown as they appear on the original answer keys. There may be inconsistencies with the formatting of these answers. In all cases, consult the Guidelines for Forms of Answers to determine the correct formatting.
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1) (-3) + (-6) = 2) (2) + (-5) = 3) (-7) + (-1) = 4) (-3) - (-6) = 5) (+2) - (+5) = 6) (-7) - (-4) = 7) (5)(-4) = 8) (-3)(-6) = 9) (-1)(2) =
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