UNIT 1 Section 2: Inequalities
1.7 Graphing Inequalities
SYMBOL DEFINITION
VERBAL EPXRESSIONS
Write an inequality to describe each number.
1. A number less than or equal to 11
2. A number greater than 3
3. A number that is at least 6
4. A number that is no less than – 7
5. A maximum number of 9
6. A number that no more than 2
Graphing Inequalities on a number line:
SYMBOLS
On a number line
UNIT 1 Section 2: Inequalities
Write an algebraic expression for each verbal expression. Then graph.
1. Z is at least negative 3.
2. k is no less than negative 1.
3. y is at most negative 2.
4. r is positive.
UNIT 1 Section 2: Inequalities
UNIT 1 Section 2: Inequalities
1.8 Solving Inequalities
Rules for solving inequalities:
Write an inequality and solve. Then check each solution.
1. A number decreased by 10 is greater than – 5.
2. A number increased by 2 is at most 6.
UNIT 1 Section 2: Inequalities
3. Negative three times a number is at least 57.
1.8 Practice
4. Two thirds of a number is no more than 4.
UNIT 1 Section 2: Inequalities
1.9 Inequalities and Real-World Problems
Warm-up: Write and solve. Then check each solution.
1. The sum of a number and 64 is greater than the product of -3 and that number.
2. Four more than the quotient of a number and 3 is at least 10.
Ex 1. The ink cartridge that Bill bought for his printer can print up to 900 pages of text.
Bill is printing handbooks that are 32 pages each. How many complete handbooks
can he print with this cartridge?
Ex 2. Madison has a goal of saving more than $1,000. She has $300 saved now, and each
month she adds $40 to that amount. The inequality 40m + 300 > 1,000 can be
solved to find the number of months, m, it will take Madison to reach her goal.
Which statement is true?
A. It will take less than 17 months for Madison to reach her goal.
B. Madison will reach her goal in 17 months.
C. Madison will reach her goal in 18 months.
D. It will take more than 18 months for Madison to reach her goal.
UNIT 1 Section 2: Inequalities
Ex 3. Ellis can spend up to $40 for gasoline and a carwash at a service station. The
carwash will cost $6.00, and gasoline cost $4.50 per gallon.
a. If g is the number of gallons of gasoline Ellis can buy, write an inequality that
represents this situation.
b. Which of the following is a true statement?
A.
B.
C.
D.
Ellis can buy over 10 gallons of gasoline.
Ellis can buy at most 7 gallons of gasoline.
Ellis can buy 6 gallons of gasoline, but not 7 gallons.
Ellis can buy 7 gallons of gasoline, but not 8 gallons.
You Try!
1. Max brought $20.00 to the arcade. Each arcade game costs $1.25 to play. He used
$6.50 of his money to buy snacks. What is the greatest number of arcade games
Max can play with the money he has left?
a. Write an inequality to find the number of arcade games, a, Max can play.
b. Solve the inequality to determine the greatest number of arcade games Max can play.
UNIT 1 Section 2: Inequalities
2. A warehouse elevator can hold at most 1,750 pounds. A 200-pound worker loads
the elevator with boxes that weigh 75 pounds each. The inequality 75b + 200 ≤
1,750 describes the maximum number of boxes the worker can put on the elevator
if he is also on the elevator. Which statement is true?
A.
B.
C.
D.
He can load at least 20 boxes.
He can load at most 20 boxes.
He can load at least 21 boxes.
He can load at most 21 boxes.
3. Jenny mows lawns to earn money. She wants to earn at least $200 to buy a new
stereo system. If she charges $12 a lawn, at least how many lawns does she need
to mow?
4. The admission fee to a state fair is $5.00. Each ride costs an additional $1.50. If
Pat does not want to spend more than $20. How many rides can he go on?
UNIT 1 Section 2: Inequalities
1.10 Compound Inequalities
Warm Up:
a. Graph x ≥ 3
b. Graph x ≤ 7
c. Find a number that would satisfy both of these inequalities.
Inequalities with AND
A compound inequality graphs _____________ inequalities on the same graph.
Ex 1. Graph x ≥ 3 AND x ≤ 7
An AND inequality graphs the _______________________ of two inequalities.
Compact form:
The two inequalities above can also be written as:
Ex 2. Rewrite the compound inequalities. Then graph.
a. x < 3 and x > - 2
b. – 4 ≤ x ≤ 6
UNIT 1 Section 2: Inequalities
Ex 3. Separate the compound inequality into two inequalities. Solve and graph.
a. -2 ≤ 𝑥 − 3 ≤ 4
b. 12< 𝑥 + 9 < 15
Inequalities with OR
A compound inequality containing or is true if ____________________________
of the inequalities is true.
Ex 1. Graph x >2 OR x ≤ - 1
Ex 2. Most snakes live where the temperature ranges from 75℉ to 90℉. Write and graph
an inequality to represent temperatures where snakes will not thrive.
UNIT 1 Section 2: Inequalities
UNIT 1 Section 2: Inequalities
1.11 Special Cases for Compound Inequalities
Special Cases for AND
Ex 1. Graph 28 <7x < - 14
Conclusion:
Ex 2. Graph 3x ≥ 15 AND -34 ≤ 17x
Conclusion:
UNIT 1 Section 2: Inequalities
Special Cases for OR
Ex 1. Graph 6 + 2x >12 OR 3x + 8 < 20
Conclusion:
Ex 2. Graph 2x ≥ 4 OR x – 4 ≥ 1
Conclusion:
UNIT 1 Section 2: Inequalities
UNIT 1 Section 2: Inequalities
1.12 Absolute Value Inequalities
Warm-up: Find three values of x that are solutions to |𝑥| ≥ 4
Ex 1. Graph |𝑥| ≥ 4
Ex 2. Solve and graph
a. |4𝑥 − 3 | > 7
b. |2𝑥 + 1| < 8
UNIT 1 Section 2: Inequalities