How do you solve #\frac { 5n } { 4} - \frac { n } { 2} = \frac { - 3} { 4}#?

1 Answer
smendyka
Mar 14, 2018

See a solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(4)# to eliminate the fractions while keeping the equation balanced. #color(red)(4)# is used because it is the Least Common Denominator of the three fractions:

#color(red)(4)((5n)/4 - n/2) = color(red)(4) xx -3/4#

#(color(red)(4) xx (5n)/4) - (color(red)(4) xx n/2) = -12/4#

#(20n)/4 - (4n)/2 = -3#

#5n - 2n = -3#

Next, combine like terms on the left side of the equation:

#(5 - 2)n = -3#

#3n = -3#

Now, divide each side of the equation by #color(red)(3)# to solve for #n# while keeping the equation balanced:

#(3n)/color(red)(3) = -3/color(red)(3)#

#1n = -1#

#n = -1#

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