Basics of Inequalities
What are the 4 inequality signs?
less than, less than or equal to, greater than, greater than or equal to
State the inverse for the problem:
x + 4 > -1
subtract 4
When do you flip the inequality sign?
when multiplying or dividing by a negative number
or if the variable is on the right
Write an inequality:
There were at least 500 people in attendance.
x ≥ 500
What is another phrase that means greater than?
above or more than
Write an inequality:
It will rain no more than 2 inches.
x ≤ 2
Solve:
16 > x + 9
x < 7
Solve: -4x > -32
x < 8
Write and solve an inequality.
You must have at least $40 in your bank account. You currently have $23. How much more do you need?
x ≥ $17
What are 3 solutions to x ≥ -5?
answers vary
What is a number that makes the inequality true?
solution
Solve and graph:
17 + x < -15
x < -32 open dot, left
Solve and graph:
x/-2 < 9
x > -18 open dot, right
Write a compound inequality:
There were more than 15 people, but less than 20 people in class today.
15 < x < 20
Graph -1 ≤ x < 3
closed dot -1, open dot 3, shade between
Graph: t > 6 or t < -1
Solve and graph:
-16 + x > -15
x > 1 open dot, right
Solve and graph:
-9 < x/-5
x < 45
Write and solve an inequality:
The area of a rectangle is at least 160 square inches. If the length is 20 inches, find the width.
x ≥ 8 inches
Graph x < -4 or x > 2
open dots, shade outward
State 2 phrases for each inequality symbol:
<, ≤, >, ≥
answers vary
Write and solve an inequality:
You and a friend need at least 4,000 points for a game. You have 1650 points and your friend has 1832 points. How many more do you need?
x ≥ 512 points
Write and solve an inequality:
A car averages at most 26 miles per gallon. If you can drive at most 416 miles, how many gallons are in the tank?
x ≤ 16 gallons
The perimeter is at most 32 feet. Find x.
Sides are 8, 7, x, x + 1
x ≤ 8 feet
The perimeter is more than 18 inches. Find x.
Sides are 8, 3, x + 1
x > 6 inches