How do you solve #x- \frac { x + 1} { 5} = \frac { x + 3} { 2} - 2#?

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Answer 1 · 2017-05-22T20:56:49

#x=-1#

First, multiply by 10 to get rid of the denominators (since the LCD of 2 and 5 is 10).

#x-(x+1)/5 = (x+3)/2 - 2#

#10x - 2(x+1) = 5(x+3) - 20#

Now distribute.

#10x - 2x - 2 = 5x + 15 - 20#

Next, group together all the #x# terms and all of the integer terms.

#8x - 2 = 5x - 5#

Subtract #5x# from both sides.

#3x-2=-5#

Add #2# to both sides.

#3x = -3#

And finally divide by 3.

#x=-1#

Final Answer