How do you solve #5/7x-3/14=-3/8x+3/4#?

1 Answer
May 11, 2018

#x=54/61#

Explanation:

The easiest way to solve this is to get rid of the denominators first.
The least common multiple of 7, 14, 8 and 4 would be #7*8=4*14=56#.

Therefore, multiply both sides with 56=4*14:
#(5/7x-3/14)*4*14=(-3/8x+3/4)*8*7#

Simplifying we get:
#5*8x-3*4=-3*7x+3*14#
or: #40x-12=-21x+42#

Adding #21x+12# to both sides to get the x terms to the left and the constants to the right, we get:
#40x+21x= 42+12#
#61x=54#
Dividing on 61 on both sides we get
#x=54/61#

As #61# is a prime number, we cannot simplify this more .