Algebra Demystified 2nd Ed

Chapter 9 linear inequaliTieS 333

We begin by “clearing the fraction,” so we multiply each quantity by 4.

2 51

4

6

42 4

1

51

4

46

85124

111

95

< - <

<⋅- <

<-<

+++

<<

x

x

x

x

() ()

225

9

5

5

5

25

5

9

5

5 9

5

5

<<

<<











x

x , 

PRACTICE

Solve the double inequality and give your solution in interval notation.

1. 14 < 2x < 20


2. 5 ≤ 3x – 1 < 8


3. –2 ≤ 3x – 4 < 5


4. −4 < −2x + 6 < 4


5. 0.12 ≤ 4x –1 < 1.8


6. 4 < 3(−2x + 1) ≤ 7


7. −1 < −6x + 11 < 1
   8.^7
   8

1

4

  <  x 2 ≤ 

9. 8 ≤ 4.5x – 1 ≤ 11


10. –≤ 6  +^2  <
    3

x 40 

11. –< 1  25 –  < 
    3

x^1

✔SOLUTIONS

1. 14 220
   14
   2

2

2

20

2

710710

<<

<<

<< ()

x

x

x ,

PRACTICE

Solve the double inequality and give your solution in interval notation.