1

Ex. 6 Solve: 12

32

xx

)2)((1)2)((2

3)2)((

2

xxxx

xxx

xMultiply by common

denominator

2(x – 2) = 3x – (x)(x – 2)

2x – 4 = 3x – x2 + 2x

x2 – 3x – 4 = 0

(x – 4)(x + 1) = 0

x = 4, – 1

2

Ex. 7 Solve: |x2 – 3x| = –4x + 6

x2 – 3x = –4x + 6–(x2 – 3x) = –4x + 6

x2 + x – 6 = 0

(x + 3)(x – 2) = 0

x = -3, 2

|(-3)2 - 3(-3)| = -4(-3) + 6

18 = 18 so -3 good

|(2)2 - 3(2)| = -4(2) + 6

2 = -2 so 2 not good

–x2 + 3x = –4x + 6

0 = x2 – 7x + 60 = (x – 6)(x – 1)

x = 6, 1

|(6)2 - 3(6)| = -4(6) + 6

18 = -18 so 6 not good

|(1)2 - 3(1)| = -4(1) + 6

2 = 2 so 1 good

3

Ex. 8 A ski club chartered a bus for a skit trip at a cost of $480. In an attempt to lower the bus fare per skier, the club invited nonmembers to go along. After five nonmembers joined the trip, the fare per skier was decreased by $4.80. How many club members are going on the trip?

(Cost per skier)(# of skiers) = cost of trip

(480/x – 4.80) (x + 5) = 480

x

x8.4480 (x + 5) = 480

(480 – 4.8x)(x + 5) = 480x

480x + 2400 – 4.8x2 – 24x = 480x

– 4.8x2 – 24x + 2400 = 0

x2 + 5x – 500 = 0

(x – 20)(x + 25) = 0

x = 20, -25

4

Compound Interest

• A= future value

• P = present value

• r = interest rate

• n = times compounded / year

• t = years

*

1n t

rA P

n

5

Ex. 9 When you were born, your grandparents deposited $5000 in a long-term investment in which the interest was compounded quarterly. Today, on your 25th birthday, the value of the investment is $25,062.59. What is the annual interest rate for this investment?

254

41500059.062,25

r

100

410125.5

r

4

10125.5 1001 r

4101625.1

r

401625.

r

r065.0

%5.6r