1. Algebra 1B – Name: _________________________
Unit 4A Applications & Keystone Problems Date: __________________________
_____MC 1) A baseball team had $1000 to spend on supplies. The team spent $185 on a new bat. New baseballs cost $4 each. The inequality b ≤ 1000 can be used to determine the number of new baseballs (b) that the team can purchase. Which statement about the number of new baseballs that can be purchased is true?
A) The team can purchase 204 new baseballs.
B) The minimum number of new baseballs that can be purchased is 185.
C) The maximum number of new baseballs that can be purchased is 185.
D) The team can purchase 185 new baseballs, but this number is neither the maximum or minimum.
_____MC2) What is the graph of |2x - 3| < 5?
_____MC3) What is the solution of the absolute value inequality |x + 3| ≥ 10?
a) -13 ≤ x ≤ 7
b) x ≥ 7
c) x ≤ -13 or x ≥ 7
d) x ≤ 7 or x ≥ -13
_____MC4) Which of the following values for x is NOT part of the solution set for |x + 1| < 4 ?
a) x = -4
b) x = 4
c) x = 1
d) x = -1
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2. The graph shows the solution set of which inequality?
_____MC5) The solution set of an inequality is graphed on the number line below.
The graph shows the solution set of which inequality?
A) 2x + 5 ≤ -1 B) 2x + 5 < -1
C) 2x + 5 > -1 D) 2x + 5 ≥ -1
_____MC6) A ticket to a baseball game costs $20. Each soda sold at the game costs $5. Shawn may spend no more than $50. He buys 1 ticket and x sodas. Shawn represents this situation with the inequality shown below.
5x + 20 ≤ 50
The solution of the inequality is x ≤ 6. Which statement best describes the solution of the inequality?
A) Shawn buys 6 or fewer sodas. B) Shawn buys 6 or fewer tickets.
C) Shawn buys 1 ticket and 5 sodas. D) Shawn has less than or equal to $6 remaining when he leaves the game.
MC7) Jason decided that he will sell his stocks if their value per share (x) goes below $5 or above $15.
_____MC7A) Which compound inequality represents the values at which Jason will SELL his stocks?
A) x > $5 or x < $15 B) x < $5 or x > $15
C) x > $5 and x < $15 D) x < $5 and x > $15
_____MC7B) Which compound inequality represents the values at which Jason will KEEP his stocks?
A) 5 < x < 15 B) 5 > x > 15
C) x < 15 D) 5 ≤ x ≤ 15
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3. ____MC8) A compound inequality is shown below.
What is the solution of the compound inequality?
5 < 2 – 3y < 14
A) -4 > y > -1 B) -4 < y < -1
C) 1 > y > 4 D) 1 < y < 4
____MC9) An inequality is shown below.
4x + 2 < 2x + 9
Which graph shows the solution of the inequality?
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4. CR1) On your basketball team, the starting players' scoring averages are between 8 and 22 points per game.
a) Write a compound inequality to describe the scoring averages for the players.
b) Write an absolute value inequality describing the scoring averages for the players.
c) Solve the absolute value inequality you wrote in part b. It should match your answer in part ___.
CR2) The test scores in your class range from 60 to 100.
a) Write a compound inequality to describe the test scores.
b) Write an absolute value inequality describing the test scores.
c) Solve the absolute value inequality you wrote in part b. It should match your answer in part ___.
CR3) Your car averages 28 miles per gallon in the city. The actual mileage varies from the average by at most 4 miles per gallon.
a) Write an absolute value inequality that shows the range for the mileage your car gets.
b) Solve the absolute value inequality that you wrote in part a.
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5. CR4) Rolando drives at least 40 miles but less than 60 miles each week.
A) Graph the compound inequality representing all of the possible distances Rolando could drive for 8 weeks.
B) Explain why you chose to use the symbols you used for the endpoints of the compound inequality in part A.
Rolando buys at least 8.5 but no more than 11 gallons of gas each week. The price of gas has ranged from $2.40 to $2.65 per gallon each week.
C) Write an inequality to model all of the possible amounts of money (m) Rolando spends on gas each week. Show or explain all your work.
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6. CR5) You work in the quality control department of a manufacturing company. The diameter of a drill bit must be between 0.62 inch and 0.63 inch.
a) Write a compound inequality to represent this requirement.
b) Write an absolute-value inequality to represent this requirement.
c) A bit has a diameter of inch. Does it meet the requirement?
CR6) A quality control inspector for a paper cup manufacturer must make sure that consecutive paper cups are able to be stacked. So, a paper cup that is supposed to have a 6.35 cm diameter has a tolerance of 0.1 cm.
a) Write an absolute value inequality to represent the requirement.
b) Solve the absolute value inequality and write it the answer as a compound inequality.
CR7) The cruiser weight division in boxing is centered at 183 pounds. A boxer's weight can be as much as 7 pounds more than or less than 183 pounds.
a) Write an absolute-value inequality for this weight requirement.
b) Solve the absolute value inequality and write the answer as a compound inequality.
CR8) The absolute value inequality |t | ≤ 0.6 is one model for normal body temperatures of an adult where t is measured in degrees Fahrenheit.
a) Solve the inequality and graph your solution.
b) Describe the range of normal body temperatures in a sentence.
c) Is a temperature of 99.5°F considered normal according to this model? Why or why not?
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