Algebra Demystified 2nd Ed

200 algebra De mystif ieD

5.^34 xx−+=− 31 1 54 x 203

The LCD is 60.

603

4

1

3

1604

5

3

20

603

4

60

xx x

x

 −+







=−















−^11

3

601604

5

60 3

20

45 20

xx

xx









+=







− 







−

()

++= −

+= −

−−

=−

++

=

60 48 9

25 60 48 9

25 25

60 23 9

99

69 23

x

xx

xx

x

xx

x

x

69

23

3

=

=

Decimals

Because decimal numbers are fractions in disguise, the same trick can be used to “clear

the decimal” in equations with decimal numbers. Count the largest number of digits

behind each decimal point and multiply both sides of the equation by 10 raised to

this power. This will change all the numbers in the equation to whole numbers.

EXAMPLES

Solve the equation by first clearing the decimal.

0.25x + 0.6 = 0.1

Because there are two digits behind the decimal in 0.25, we need to multi-

ply both sides of the equation by 10^2 = 100. Remember to distribute the

100 inside the parentheses.

10002506 10001

100025 10006 100

(. .) (.)

(. )(.) (

x

x

+=

+= 001

25 60 10

60 60

25 50

50

25

2

.)

x

x

x

x

+=

−−

=−

=−

=−

EXAMPLES

Solve the equation by first clearing the decimal.

0.25

EXAMPLES

Solve the equation by first clearing the decimal.