Absolute Values
How many solutions does the equation 2+3|7x+5| = 5 have?
2
Yes.
Write [2, 6) in the set-builder form using an inequality.
{x|2 ≤ x < 6}
What form is the following representation of a set: {1, 5, 2, b}?
The roster form.
What's the intersection between {a, b, c} and {d, e, f}?
{ }, the empty set.
Solve 2 + |n| ≤ 5.
-3 ≤ n ≤ 3.
The Freshmen class is sponsoring a bake sale. If its goal is to raise at least $150, how many pastries must it sell at $3 each to meet that goal? Write and solve an inequality.
If x is the number of pastries sold, 3x ≥ 150. x ≥ 50.
How many solutions does the inequality -5 ≤ x < 0 have?
Infinitely many.
If the universal set is {1, 3, 5, 7, 9} and P = {1, 3, 5}, what is P’?
{7, 9}
What are all the subsets of {1, 3}?
{ }, {1}, {3}, {1,3}
I am chaperoning my little sister and can't be more than 5 feet away from her. My little sister is 20 feet from a fountain, how far away can I be from the fountain? Write an inequality using absolute values!
|x - 20| ≤ 5, 15 ≤ x ≤ 25. I am from 15 to 25 feet away from the fountain.
Solve x + 5 ≤ 2x + 3 < 14.
2 ≤ x < 11/2
An isosceles triangle has at least two congruent sides. The perimeter of a certain isosceles triangle is at most 12 in. The length of each of the two congruent sides is 5 in. What are the possible lengths of the remaining side?
Let the length of the remaining side be x. Then 2*5 + x ≤ 12. x ≤ 2.
Find a subset of [5, 8) that has 3 elements.
What's the intersection of [1,5) and (2, 10]?
(2, 5)
Start from 150 feet away, a person on a bicycle rides towards a checkpoint and then passes it. The rider travels 60 feet per second. Write an expression in time variable t that describes the rider’s distance from the checkpoint. At what times is the rider 30 feet away from the checkpoint?
|150 - 60t| = 30, t = 2 or t = 3. Exactly 2 seconds after the start, the rider is 30 feet to the checkpoint; exactly 3 seconds after the start, the rider is 30 feet from the checkpoint.
You scored 78, 87, and 79 on your first three tests. What possible scores can you earn on the last test to earn a test average between 84 and 86?
92 ≤ x ≤ 100.
How many numbers are in the interval [-5, 0)?
Infinitely many.
What's the intersection between all the even numbers and all the odd numbers?
{ }
Solve 6-3|2+4x| ≤ 3.
x ≥ -1/4 or x ≤ -3/4
If the universal set is all the real numbers, what is the complement of [2, 5)?
Oops can't enter equations so here's the word version of it: (negative infinity, 2) union [5, infinity)
There are 24 items in sets A, B, C in total. 5 items are in A only; 10 items are in B; 3 items are in both A and B; 2 items are in both B and C; 4 items are in both A and C; 2 items are in all of A, B, C. How many items are in C?
11