How do you solve #-3/4x+5/14=-2# by clearing the fractions?

1 Answer
Feb 5, 2017

Answer:

See the entire solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(28)# to eliminate the fractions while keeping the equation balanced. #color(red)(28)# is the lowest common denominator of the two fractions.

#color(red)(28)(-3/4x + 5/14) = color(red)(28) xx -2#

#(color(red)(28) xx -3/4x) + (color(red)(28) xx 5/14) = -56#

#(cancel(color(red)(28))7 xx -3/color(red)(cancel(color(black)(4)))x) + (cancel(color(red)(28))2 xx 5/color(red)(cancel(color(black)(14)))) = -56#

#-21x + 10 = -56#

Next, subtract #color(red)(10)# from each side of the equation to isolate the #x# term while keeping the equation balanced:

#-21x + 10 - color(red)(10) = -56 - color(red)(10)#

#-21x + 0 = -66#

#-21x = -66#

Now, divide each side of the equation by #color(red)(-21)# to solve for #x# while keeping the equation balanced:

#(-21x)/color(red)(-21) = (-66)/color(red)(-21)#

#(color(red)(cancel(color(black)(-21)))x)/cancel(color(red)(-21)) = (3 xx 22)/color(red)(3 xx 7)#

#x = (color(red)(cancel(color(black)(3))) xx 22)/color(red)(cancel(3) xx 7)#

#x = 22/7#