copyright © by holt, rinehart and winston. all rights reserved. (additional slides created/edited...

Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

(Additional slides created/edited

by Mr. Weidinger EWHS Goldsboro, NC)

Objectives• State and use symbols of inequality.• Solve inequalities that involve addition and

subtraction.

6.1 Solving Inequalities

NCSCOS

• 4.01 – Use linear functions inequalities to model and solve problems.




Rules and Properties


a is less than b. a < ba is greater than b. a > ba is less than or equal to b. a b

a is greater than or equal to b. a ba is greater than b and less than c. b < a < c

a is greater than or equal to b and b a c less than or equal to c.a is not equal to b. a b

Statements of InequalityStatements of Inequality



by Mr. Weidinger EWHS Goldsboro, NC)6.1 Solving Inequalities

Inequality Addition and Subtraction

Let a, b, and c be real numbers.

If a < b, then a + c < b + c

If 4 < 5

then, 4 + 3 < 5 + 3

If a < b, then a c < b c

If 7 < 8

then, 7 3 < 8 3

7 < 8

4 < 5




Inequality Addition and Subtraction

Let a, b, and c be real numbers.

If a > b, then a + c > b + cIf 6 > 5

then 6 + 1 > 5 + 1

If a > b, then a c > b cIf 9 > 3

then 9 2 > 3 2

7 > 6

7 > 1




Graphing number lines:

Greater than or equal to:- use a closed circle on a number line:

Less than or equal to:

- use a closed circle on a number line:

Greater than:- use an open circle on a number line:

Less than:

- use an open circle on a number line:




Graph the inequalities:

x 3

x 0

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

x 5

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7x -4




Solve inequalities and graph.

x + 12 16x 4

x – 8 2x 10

x – 5 2x 7

6 8 10 12 14 16 18

1 3 5 7 9 11 13




Solve inequalities and graph

x + 4 12x 8

x – 6 2

x 8

4 6 8 10 12 14

2 4 6 8 10 12

5 x – 3

2 4 6 8 10 12 x < 8




Solve the inequalities

18 + x –6

x –24 -30 -28 -26 -24 -22 -20 -18

7 + x –6 x –13 -23 -21 -19 -17 -15 -13 -11

x + 4 2

-8 -6 -4 -2 0 2 x -2





x – >

x >

74

34

52

–2 –1 0 1 2 3 4 5 6

x +

x –

23

59

19

–1 –.75 –.25 0 .25 .50 .75





-23 -21 -19 -17 -15 -13 -11

1)

2 3 4 5 6 7 8 9 10 12 14

2)

14 16 18 20 22 24 26

3)

x -19

x 9

x 17





4)

3 5 7 9 11 13 15

5)

4 6 8 10 12 14 x 14

x 5

6)-6 -4 -2 0 2 4 6

x -4

-4 -3 -2 -1 0 1 2 3 4 5 6 7 8

7) x -3




Michael can spend at most $3.10 for lunch. He buys a hamburger and a drink for $2.15. Write an inequality that models how much Michael can spend on dessert and stay within his spending limits.

d + $2.15 = $3.10

Let ‘d’ be the amount Michael can spend on dessert.


There are two possible equations:

d + $2.15 $3.10d + $2.15 $3.10

d $0.95

Michael can spend no more than $0.95 on dessert.




Trisha has only $6.23 to spend for lunch. She buys a cheeseburger, fries, and a drink for $4.69. Write an inequality that models how much Trisha can spend on a milk shake and stay within her spending limits.

m + $4.69 = $6.23

Let ‘m’ be the amount Trisha can spend on a milk shake.



m + $4.69 $6.23m + $4.69 $6.23

m $1.54

Trisha can spend no more than $1.54 to buy a milk shake.




Anne can spend at most $15.00 when she goes to see a movie. She has to spend $1.25 each way for a subway ride, and the movie ticket is $7.00. Write an inequality that models how much Anne can spend on refreshments and stay within her spending limits.

r + $1.25 + 1.25 + 7.00 = $15.00

Let ‘r’ be the amount Anne can spend on refreshments.



r + $9.50 $15.00r + $9.50 $15.00

r $5.50

Anne can spend no more than $5.50 on refreshments.




A school auditorium can seat 450 people for graduation. The graduates will use 74 seats. Write and solve an inequality to describe the number of additional people who can be seated in the auditorium.


x + 74 450 x 376

Write and solve an inequality to describe the number of additional seats in an auditorium if the school auditorium can seat 450 people for graduation. Graduates will use 74 seats and their personal family and friends will use 370 seats. x + 444 450 x 6

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