How do you solve #11/3x-1/4=2#?

1 Answer
Jan 9, 2017

Answer:

#x = 27/44#

Explanation:

Your first goal here is to make sure that all the fractions have the same denominator. As given, the equation looks like this

#11/3x - 1/4 = 2/1#

Now, the common denominator for #3#, #4#, and #1# is #12#, so you will need to multiply the first fraction by #1 = 4/4#, the second fraction by #1 = 3/3#, and the third fraction by #1 = 12/12#.

This will get you

#11/3x * 4/4 - 1/4 * 3/3 = 2/1 * 12/12#

You now have three fractions with equal denominators

#(11 * 4)/12x - (1 * 3)/12 = (2 * 12)/12#

#44/12x - 3/12 = 24/12#

You can now focus exclusively on the numerators and say that

#44 * x - 3= 24#

Add #3# to both sides of the equation

#44 * x - color(red)(cancel(color(black)(3))) + color(red)(cancel(color(black)(3))) = 24 + 3#

#44 * x = 27#

Divide both sides of the equation by #44# to get

#(color(red)(cancel(color(black)(44))) * x)/color(red)(cancel(color(black)(44))) = 27/44#

#x = 27/44#

Do a quick double-check to make sure that the calculations are correct

#11/3 * 27/44 - 1/4 = 2#

#(11 * 9)/44 - 1/4 = 2#

#9/4 - 1/4 = 2#

#8/4 = 2" "color(darkgreen)(sqrt())#