How do you solve #1\frac { 7} { 8} x + \frac { 4} { 5} + 1\frac { 1} { 4} x = - \frac { 109} { 20}#?

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Answer 1 · 2017-06-04T18:45:02

#x=-2#

First, convert all the fractions to #d//e# form

#15/8x+4/5+5/4x=-109/20#

Next, combine like terms with #x# in it.

#15/8x+5/4x+4/5=-109/20#

#25/8x+4/5=-109/20#

Subtract #4/5# from both sides

#25/8x+4/5color(red)(-4/5)=-109/20color(red)(-4/5)#

This gives

#25/8x=-25/4#

Finally, multiply both sides by #8/25# to get the #x# by itself:

#color(blue)(8/25)xx25/8x=color(blue)(8/25)xx-25/4#

#x=-2#