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Worksheets

Basic Quadratic Inequalities

Total questions: 12

Worksheet time: 6mins

Name
Class
Date
1.

Solve the following

x29x^2\le9   

a)

3x3-3\le x\le3  

b)

3<x<3-3<x<3  

c)

x>3 or x<3x>3\ or\ x<-3  

d)

x3 or x3x\ge3\ or\ x\le-3  

e)

x3 or x3x\le3\ or\ x\ge-3  

2.

Solve the following

x2<9x^2<9   

a)

3x3-3\le x\le3  

b)

3<x<3-3<x<3  

c)

x>3 or x<3x>3\ or\ x<-3  

d)

x3 or x3x\ge3\ or\ x\le-3  

e)

x3 or x3x\le3\ or\ x\ge-3  

3.

Solve the following

x29x^2\ge9   

a)

3x3-3\le x\le3  

b)

3<x<3-3<x<3  

c)

x>3 or x<3x>3\ or\ x<-3  

d)

x3 or x3x\ge3\ or\ x\le-3  

e)

x3 and x3x\ge3\ and\ x\le-3  

4.

Solve the following

x2>9x^2>9   

a)

3x3-3\le x\le3  

b)

3<x<3-3<x<3  

c)

x>3 or x<3x>3\ or\ x<-3  

d)

x3 or x3x\ge3\ or\ x\le-3  

e)

x>3 and x<3x>3\ and\ x<-3  

5.

Solve the following

x21<3x^2-1<3   

a)

2x2-2\le x\le2  

b)

2<x<2-2<x<2  

c)

x>2 or x<2x>2\ or\ x<-2  

d)

x2 or x2x\ge2\ or\ x\le-2  

e)

x2 or x2x\le2\ or\ x\ge-2  

6.

Solve the following

x21<3x^2-1<3   

a)

2x2-2\le x\le2  

b)

2<x<2-2<x<2  

c)

x>2 or x<2x>2\ or\ x<-2  

d)

x2 or x2x\ge2\ or\ x\le-2  

e)

x2 or x2x\le2\ or\ x\ge-2  

7.

Solve the following

2x2>82x^2>8   

a)

2x2-2\le x\le2  

b)

2<x<2-2<x<2  

c)

x>2 or x<2x>2\ or\ x<-2  

d)

x2 or x2x\ge2\ or\ x\le-2  

e)

x>2 and x<2x>2\ and\ x<-2  

8.

Solve the following

12x212\frac{1}{2}x^2\le\frac{1}{2}   

a)

1x1-1\le x\le1  

b)

1<x<1-1<x<1  

c)

x>1 or x<1x>1\ or\ x<-1  

d)

x1 or x1x\ge1\ or\ x\le-1  

e)

x1 or x1x\le1\ or\ x\ge-1  

9.

Solve the following

4x2+1654x^2+1\ge65   

a)

4x4-4\le x\le4  

b)

4<x<4-4<x<4  

c)

x>4 or x<4x>4\ or\ x<-4  

d)

x4 or x4x\ge4\ or\ x\le-4  

e)

x4 and x4x\ge4\ and\ x\le-4  

10.

Solve the following

8>1+x28>-1+x^2   

a)

3x3-3\le x\le3  

b)

3<x<3-3<x<3  

c)

x>3 or x<3x>3\ or\ x<-3  

d)

x3 or x3x\ge3\ or\ x\le-3  

e)

x3 and x3x\ge3\ and\ x\le-3  

11.

Solve the following

512x2+151\le2x^2+1   

a)

5x5-5\le x\le5  

b)

5<x<5-5<x<5  

c)

x>5 or x<5x>5\ or\ x<-5  

d)

x5 or x5x\ge5\ or\ x\le-5  

e)

x5 and x5x\ge5\ and\ x\le-5  

12.

Solve the following

77x22147\le\frac{7x^2-21}{4}   

a)

7x7-\sqrt[]{7}\le x\le\sqrt[]{7}  

b)

7<x<7-\sqrt[]{7}<x<\sqrt[]{7}  

c)

x>7 or x<7x>\sqrt[]{7}\ or\ x<-\sqrt[]{7}  

d)

x7 or x7x\ge\sqrt[]{7}\ or\ x\le-\sqrt[]{7}  

e)

x7 and x7x\ge\sqrt[]{7}\ and\ x\le-\sqrt[]{7}