How do you solve #2/5 + 1/4 = x -1/2#?

1 Answer
May 2, 2017

See the entire solution process below:

Explanation:

First multiply each side of the equation by #color(red)(20)# to eliminate all of the fractions. #color(red)(20)# is the Lowest Common Denominator for all of the fractions:

#color(red)(20)(2/5 + 1/4) = color(red)(20)(x - 1/2)#

#(color(red)(20) xx 2/5) + (color(red)(20) xx 1/4) = (color(red)(20) xx x) - (color(red)(20) xx 1/2)#

#(cancel(color(red)(20)) 4 xx 2/color(red)(cancel(color(black)(5)))) + (cancel(color(red)(20)) 5 xx 1/color(red)(cancel(color(black)(4)))) = 20x - (cancel(color(red)(20)) 10 xx 1/color(red)(cancel(color(black)(2))))#

#8 + 5 = 20x - 10#

#13 = 20x - 10#

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

#13 + color(red)(10) = 20x - 10 + color(red)(10)#

#23 = 20x - 0#

#23 = 20x#

Now, divide each side of the equation by #color(red)(20)# to solve for #x# while keeping the equation balanced:

#23/color(red)(20) = (20x)/color(red)(20)#

#23/20 = (color(red)(cancel(color(black)(20)))x)/cancel(color(red)(20))#

#23/20 = x#

#x = 23/20#