6-3A Solving Multi-Step Inequalities

Algebra 1 Glencoe McGraw-Hill Linda Stamper

A multi-step inequality is solved by transforming the inequality more than one time. Undo addition or subtraction before undoing multiplication or division or you may make the problem more complicated to solve. Always remember the basic rule when isolating the variable:

Whatever you do to one side of the

inequality sign, you must also do to the

other side of the inequality sign.

>

Solve –9 – x < – 6.

Write the inequality. 6 x9

Undo the subtraction 9 93 x Undo the negative

variable, 1 1/

3 x

1reverse inequality symbol and simplify.

Solve.

5 3y2 1) 3 3

2y2 2 2

1y >

11 x21 2) 1 1

21 x2 2 2

/

6 x

3) Four times a number plus twelve is less than or equal to negative seven more than three.4) Two more than half a number is greater than twenty-seven.

Write an inequality and then solve.

3) Four times a number plus twelve is less than or equal to negative seven more than three.

4) Two more than half a number is greater than twenty-seven.

Write an inequality and then solve.

73 12n4

12 1216n4

4 4 4n

4 12n4

272n21

2 2

25n21 2 2

50n

Are your inequality signs in a

line?

Solve.

17

4 17x9x2)1

3x

174 17x7

21x7 7 7

+–+– 279 x5 x2 –x2

6x

x5

2745x3 45 45

2745

18x3 3 3

– 279 x5 x2)2

>/

>/

Solve.

>

5h5419 3)

55

h54 42

4

5

4

5

h30

/

30 h

>

83m12

487 4)

838

3

m124 8

4

4

12

4

12

m23

/

23 m

Solve.

<

922x34 5)

8928x12

84x12 12

8

12 7x

/

784x36 6)

247824x18

54x18 18

24

18 3x

Solve.

>

27.0y05.083.0 7)

10010027y5 38 2727

y5110 /

22 y

27.0y05.083.0

5 5 y22

<

9.0n6.01.2 8)

10109 n621

212112n6 / 2 n

9.0n6.01.2

6 6

Solve.

18x5312 10)

10x

9 95415x

15 1539x

1

6915x)9

6915x 18 18

x536

3

5

3

5

x10>/

82x54

45

45

102x 2 2

12x

21

82x54)11

Solve.

2x10312

310

310

2x40 2 2

x38

14

2x10312)12

38x

6-A3 Pages 311–313 #12–23,59–61.