Inequalities & their Graphs
Which number(s) are a solution to the following inequality: 4x - 3 ≤ 5
a. 2 b. 3 c. -1
a: 2 & c: -1
Solve and graph:
8x > -24
x > -3
GRAPH
Solve and graph:
x + 7 ≤ 3x - 1
x ≥ 4
GRAPH
Solve and graph:
8 < x + 3 < 10
5 < x < 7
GRAPH
Solve:
3 | x | + 2 = 11
x = 3 OR x = -3
Describe what the following graph looks like, and then draw it:
-6 ≤ x
Closed circle at -6, arrow going to the right
Solve and graph:
4 - a > 15
a < - 11
GRAPH
Solve and graph:
(9 - 2x) / 3 < 5
x > -3
GRAPH
Solve and graph:
6x - 15 ≤ 9 OR 10x > 84
x ≤ 4 OR x > 8.4
GRAPH
Solve:
| 2x + 3 | = 9
x = 3 OR x = -6
Which number(s) are a solution to the following inequality: 5 ( 2q - 8 ) ≥ 7
a. -2 b. 9/2 c. 6
c: 6
Solve and graph:
-12x ≤ 54
x ≥ - 4.5
GRAPH
A technical-support company charges $10 per month plus $35 per hour of phone support. If you need to spend less than $100 per month on support, how many hours can you get? Write and solve.
10 + 35x < 100
x < 2.5 hours
Solve and graph:
2x - 3 ≤ x AND 2x + 1 ≥ x + 3
2 ≤ x ≤ 3
GRAPH
Solve and graph:
-| -6x + 2 | = 20
No Solution
Define the variable, write the inequality, and graph the following situation:
At least 350 students attended the performance over the weekend
s = students; s ≥ 350
closed circle at 350, arrow going to the right
You are reading a book with 19 chapters. How many chapters should you read each week if you want to finish the book in 5 weeks or less? Write and solve.
19/x ≤ 5
3.8 ≤ x
A sophomore class is putting on a show to raise money. If it costs $700 to rent the theater, and they charge $15 per ticket, how many tickets do they need to sell to raise at least $1000. Write and solve.
15x - 700 ≥ 1000
x ≥ 114
Water will not be liquid when it is colder than 32℉ or warmer than 212℉. Write a compound inequality
32 ≤ x ≤ 212
Solve:
-2 | x + 7 | = -10
x = -2 OR x = -12