Lesson Quiz

Lesson Presentation

Lesson 3.4Solving Inequalities using Addition or Subtraction

Skill Check

Skill Check

2. 17 23 – 5

3. ½ 1/3

>

<

>

1. 2 + 3 4

4. 31 – 6 17 + 9 <

Replace each with > or <.

Vocabulary Is a mathematical statement

formed by placing an inequality symbol between two expressions. Symbols are: <, >, <, >

With a variable is the set of all numbers that produce true statements when substituted for the variable.

Are inequalities that have the same solution.

Study Strategy

When drawing graphs of inequalities, make sure open circles and closed circles are clear and easily differentiated.Example:1. All numbers less than 72. All numbers greater than 43. All numbers less or equal to 14. All numbers greater than -4

Writing and Graphing an InequalityEXAMPLE 1Cybercafé KIS’s cybercafé charges users a minimum fee of 2000 won for internet access. Write an inequality to represent the access fee f. Then graph the inequality.

ANSWER

f > 2000

2000 0

Solving an Inequality Using SubtractionEXAMPLE 2

SOLUTION

k + 12 < -4

Solve k + 12 < -4.Graph and Check your solution.

-12 + k + 12 < -4 – 12

k < -16

-16 0

Solving an Inequality Using AdditionEXAMPLE 3

SOLUTION

-1 > y - 7

Solve -1 > y - 7.Graph and Check your solution.

7 – 1 > y – 7 + 7

y < 6

60

Writing and Solving an EquationEXAMPLE 4

Math Test On the first two tests in math class, Diana had scores of 89 and 95 points. The third math test is tomorrow, and Diana’s goal is to have a total score of 279 or higher on the three math tests in order to have an A average for this quarter. What possible scores s can she have on the test tomorrow to attain her goal? Write a verbal model.

ANSWER Diana’s possible score that she can have on the test tomorrow to attain her goal is 95 or higher.

Diana’s first math score

+Diana’s second math score

+Diana’s possible scores s

>Diana’s goal total score on 3 math tests

89 + 95 + s > 279-184 + 89 + 95 + s > 279 – 184s >

95

Lesson Quiz

1. 17 + a > 20

2. -5 > s – 1

3. A traffic reporter announced that traffic will be delayed at least 15 minutes. Write an inequality to represent this.

a > 3

s < -4

t > 15 Min

Solve the Inequality. Graph your solution.

4. Challenge Which one of these compound inequalities has a graph that is not an empty number line?

A. x > 3 and x > 5

-4 0

30

A. x > 3 and x > 5

B. y < -1 and y > 1C. z > -5 and z < -6

Closure• 1.) Give an example of an inequality

that can be solved using the addition property of inequality, and another that can be solved using the subtraction property of inequality.

a – 1 > 3 solve by addition b + 1 < 3 solve by subtraction

Closure• 2.) Celine has cats, geese, and

snakes as pets. Her animals have a total of 22 legs. If she has more cats than geese and more geese than snakes, how many of each animal does she have?

4 cats, 3 geese, and two snakes

4x = cats

2y = geese

cats > geese x is the number of

catsy is the number of geese x >

y 4x + 2y = 22

Solve by guess, Check, and revise, or by graphing.

y = -2x + 11

y < x

Lesson 3.4 Homework:pp.143-144 Exs. (12, 14, 16, 30, 32, 34, 36, 38, 40, 42, 43, 49, 50)Challenge/Bonus 44