196 algebra De mystif ieD

still struggling

a common mistake is to fail to distribute the lCD. another is to multiply only

one side of the equation by the lCD. in the first example,^45 x+=− 14 , one

common mistake is to multiply both sides by 5 but not to distribute 5 on the

lef-thand side.

5

4

5

14

414

x

x

 +







=−

+=− (incorrect)

another common mistake is not to multiply both sides of the equation

by the lCD.

54

5

14

454

x

x

 +







=−

+=− (incorrect)

in each case, the last line is not equivalent to the first line—that is, the solution

to the last equation is not the solution to the first equation.

?

In some cases, we will need to use the associative property of multiplication

with the LCD instead of the distributive property.

EXAMPLE

Solve the equation by first clearing the fraction(s).

1

3

4 1

2

()xx+=()− (^1)
The LCD is 6.
61
3
461
2
()xx+ () 1



=−




EXAMPLE
Solve the equation by first clearing the fraction(s).
EXAMPLE
Solve the equation by first clearing the fraction(s).