Everything Maths Grade 10

Exercise 4 – 6:

1.Look at the number line and write down the inequality it represents.

a)

 2  1 0 1 2 3 4 5 6 7 x

b)

0 1 2 3 4 5 6 7 8 x

c)

0 1 2 3 4 5 6 7 8 x

d)

 30  20  10 0 10 20 30 x

2.Solve forxand represent the answer on a number line and in interval notation.

a) 3 x+ 4> 5 x+ 8 b)3(x1) 2  6 x+ 4

c)

x 7

3

>

2 x 3

2

d)4(x1)< x+ 2

e)

1

2

x+

1

3

(x1)

5

6

x

1

3

f) 2 x 1 < 3

g)  5 < 2 x 3  7 h) 7(3x+ 2)5(2x3)> 7

i)

5 x 1

 6



1  2 x

3

j) 3  4 x 16

k)

 7 y

3

 5 > 7 l) 1  1  2 y < 9

m)  2 <

x 1

 3

< 7

3.Solve forxand show your answer in interval notation:

a) 2 x 1 <3(x+ 11) b)x 1 <4(x6)

c)

x 1

8



2(x2)

3

d)

x+ 2

4



2(x4)

7

e)

1

5

x

5

4

(x+ 2)>

1

4

x+ 3 f)

1

5

x

2

5

(x+ 3)

4

2

x+ 3

g) 4 x+ 3< 3 or 4 x+ 3> 5 h) 4  6 x 6  3

4.Solve for the unknown variable and show your answer on a number line.

a) 6 b 3 > b+ 2; b 2 Z b) 3 a 1 < 4 a+ 6; a 2 N

c)

b 3

2

+ 1<

b

4

 4 ; b 2 R d)

4 a+ 7

3

 5 > a

2

3

; a 2 N

For more exercises, visit http://www.everythingmaths.co.za and click on ’Practise Maths’.

1a.2FGJ 1b.2FGK 1c.2FGM 1d.2FGN 2a.2FGP 2b.2FGQ 2c.2FGR

2d.2FGS 2e.2FGT 2f.2FGV 2g.2FGW 2h.2FGX 2i.2FGY 2j.2FGZ

2k.2FH2 2l.2FH3 2m.2FH4 3a.2FH5 3b.2FH6 3c.2FH7 3d.2FH8

3e.2FH9 3f.2FHB 3g.2FHC 3h.2FHD 4a.2FHF 4b.2FHG 4c.2FHH

4d.2FHJ

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100 4.7. Solving linear inequalities