How do you solve #\frac { 3} { 7x } - \frac { 6} { 4} = \frac { 3} { 28x } - \frac { 6} { 112}#?

1 Answer
EZ as pi
Jun 30, 2017

#x = 2/9#

Explanation:

#3/(7x) -6/4 = 3/(28x)-6/112" "larr# simplify #6/112#

#3/(7x) -6/4 = 3/(28x)-3/56#

When you are solving an EQUATION which has FRACTIONS, you can get rid of the fractions immediately by multiplying each term by the LCD and then cancelling the denominators.

In this case, the LCD of #7x," " 4," " 28x" and " 56# is #" "color(red)(56x)#

#(color(red)(56x)xx3)/(7x) -(color(red)(56x)xx6)/4 = (color(red)(56x)xx3)/(28x)-(color(red)(56x)xx3)/56#

#(cancelcolor(red)(56x)^8xx3)/(cancel(7x)) -(cancel(color(red)(56))^14 xx x xx6)/cancel4 = (cancelcolor(red)((56x))^2xx3)/cancel(28x)-(color(red)(cancel56x)xx3)/cancel56#

This leaves us with:

#24-84x = 6 -3x" "larr# solve as usual

#24-6 = 84x-3x#

#18 = 81x#

#18/81 =x#

#x = 2/9#

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