Algebra Demystified 2nd Ed

Chapter 9 linear inequaliTieS 331

Because we want to solve for x, we divide all three quantities by 2.

42 12

4

2

2

2

12

2

2626

≤≤

≤≤

≤≤

x

x

x [, ]

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

6 ≤ 4 x – 2 ≤ 10

We begin by adding 2 to each quantity and then dividing each quantity
by 4.

64210

222

8412

8

4

4

4

12

4

2323

≤-≤

+++

≤≤

≤≤

≤≤

x

x

x

x [, ]

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

-<-+< 62 x 31

-<-+<

---

-<-<-

• 
  


• 
  

>-

• 
  

>-

• 
  

  
  

  
  

6231

333

92 2

9

2

2

2

2

2

9

2

x

x

x

x>><< 







11 9

2

19

2

or x , 

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

73 ≤+<x 74

7374

777

03 3

0

3

3

3

3

3

01

≤+<

---

≤<-

≤<-

≤<-

x

x

x

x [[, 01  )-