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Inequalities
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100
Solve | 2x + 3 | < 6.
What is –9/2 < x < 3/2.
100
Simplify 3(x + 4)
What is 3x + 12
100
In three more years, Miguel's grandfather will be six times as old as Miguel was last year. When Miguel's present age is added to his grandfather's present age, the total is 68. How old is each one now?
What is grandfather is 57 and Miguel is 11.
100
Give the degree of the following polynomial: 2x^5 – 5x^3 – 10x + 9
What is a fifth-degree polynomial.
100
There are 16 ducks and 9 geese in a certain park. Express the ratio of ducks to geese in all three formats.
What is 16:9, 16/9, and 16 to 9.
200
Solve | 2x – 3 | > 5
What is x < –1 and x > 4.
200
Simplify –2(x – 4)
What is –2x + 8
200
The radius of a circle is 3 centimeters. What is the circle's circumference?
What is 6pi cm.
200
Give the degree of the following polynomial: 7x^4 + 6x^2 + x
What is a fourth-degree polynomial.
200
In a certain class, the ratio of passing grades to failing grades is 7 to 5. How many of the 36 students failed the course?
What is 15 students failed.
300
Find the absolute-value inequality statement that corresponds to the inequality –2 < x < 4.
What is | x – 1 | < 3
300
Simplify –(x – 3)
What is –x + 3
300
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
What is 6 quarters, 9 dimes, and 18 nickels.
300
Evaluate 2x^3 – x^2 – 4x + 2 at x = –3
What is -49.
300
Consider those ducks and geese we counted back at the park. Their ratio was 16 ducks to 9 geese. Suppose that there are 192 ducks. How many geese are there?
What is 108 geese.
400
Find the absolute-value inequality statement that corresponds to the inequalities x < 19 or x > 24.
What is | x – 21.5 | > 2.5
400
Simplify 2 + 4(x – 1)
What is 4x – 2
400
A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?
What is Two hours: 105 mph and Three hours: 115 mph
400
Simplify (2x + 5y) + (3x – 2y)
What is 5x + 3y.
400
Solve for n: 1/2 = n/4.
What is n=2
500
Solve x + 3 < 0
What is x < –3
500
Simplify x^6 × x^5
What is x^11
500
You put $1000 into an investment yielding 6% annual interest; you left the money in for two years. How much interest do you get at the end of those two years?
What is $120 in interest.
500
Simplify –3x(4x^2 – x + 10)
What is –12x^3 + 3x^2 – 30x
500
Write these as a ratio: an inch to a foot an ounce to a pound
What is 1:12 and 1:16