MTH3200

Tutorial 3

1. Solve:

a) 3 2

41

x

x

+ i) 2543 =+ xx

b) 4

13 x

f) 3

2

(5 3)0

(8 25)

x

x

j) 543 < xx

c) 2

24 10

x

x>

g) 3 1

21

x

x

+

k) 36 =x

d) 4

3 45

x

l) 6 1

31

x

x

+

2. Write the solution for each of the following inequality in interval form and then sketch the solution on a number line.

a) 2 6 16 8x x+ + d) 4 5

1 92

x < e) 1 3

2 6x x

+

h) 4 7

2 53

xx

+ +

c) 5

13

x

x

>

+

f) 15437

3. Let , , , ,a b c d then prove:

a) ( ) ( )a b c a b c+ = + e) a b a b+ +

b) If ac bc= , and 0c , then a b= f) a b a b

c) a a a

b b b

= =

( 0)b g) a b c < iff b c a b c < < +

d) If ,a

db

= ( 0)b then a bd= h) ( ) ( ) ( )c a c a + = +