Single Inequalities
Double Inequalities
Notation
Word Problems
100
Solve the following inequality
3x+2<14
x < 4
100
Solve the following inequality:
6< -3x < 18
-6 < x < -2
100
Express the following in bracket (interval) notation:
x <-8
x ∈ ] -oo, -8[
100
In Alessandra's dance class of at least 25 students, there are 7 more students in pink skirts than in black skirts. What is the minimum number of students wearing a black skirt in the group?
There must be at least 9 students wearing black skirts.
200
Solve the following inequality
5x-1≤3x+7
x ≤ 4
200
Solve the following inequality
3<2x+4<8
-1/2<x<2
200
Express the following in bracket notation and on a number line (both must be correct to get points!):
0 le x <10
x in [0, 10 [
200
While playing soccer on the back field behind the school, Francesco noticed that it is built such that the length is 12 metres less than 4 times the width. If we know that the perimeter is at most 300 metres, what is the greatest possible width of the back field?
The width can be at most 32.4 metres.
300
Solve the following inequality:
-3(x-2) > 6x - 6(x+2)
x < 6
300
Solve the following inequality
3 <(-2x+4)/6<4
-10 < x < -7
300
Express the following in set builder notation:
x in ] -oo, -3[
{x in RR | x < -3}
300
In Kailyn's home library, she has at least 300 books and at most 630 books. If she has twice the amount of paperbacks than hardcovers, what is the range that describes the number of hardcover books she may have in her home library?
Kailyn must have at least 100, but at most 110 hard cover books.
400
Solve the following inequality:
(2x+3)/-4 > 5/2
x> -13/2
400
Solve the following inequality:
3/4 < (x+6)/2 < 5/2
-9/2 < x < -1
400
Express the following in bracket (interval) notation, and set builder notation (both must be correct to get points!) :
x in [84, oo[
{ x in RR | 84 le x}
400
Addison owns a pool shop in the community centre. She sells swimming caps for 15$ each and swimming goggles for 6$ each. One day, she sold 4 more swimming goggles than double the number of swimming caps. How many swimming caps did she sell if she made at least 960$ in sales that day?
She sold at least 35 swimming caps.
500
Solve the following inequality, presenting your answer in bracket notation:
2(x-2)-3/4(x+1) ≤ 5/6(12x+6)
x ≥ -39/35
x ∈ ]-39/35,∞]
500
Solve the following inequality:
5 < (2x+3)/3 < 3/2
-1/4 < x < 3/4
or
-0.25 < x < 0.75
500
The description: "The product of three times a number and eight times a number is greater than four times a number plus two" can be represented by which of the following inequalities:
a) (3x)(8x) > 4x + 2
b) 3x + 8x > 4x + 2
c) (3x)(8x) < 4x +2
d) 3x + 8x < 4x + 2
a) (3x)(8x) > 4x + 2
500
Massimo noticed that the captain of the Pittsburgh Penguins hockey team has scored a minimum of 36, but a maximum of 90 goals this past season. If he's scored triple the number of shorthand goals than empty net goals, what is the range that describes the amount of shorthand goals and empty net goals that he's scored?
He's scored at least 9, but at most 22 empty-net goals.
He's scored at least 27, but at most 66 short-hand goals.