How do you solve #(5x+6)/5 = (4x+10)/3#?

1 Answer
Stefan V.
Oct 18, 2015

#-32/5#

Explanation:

Your goal here is to isolate #x# on one side of the equation.

To do that, start by finding the common denominator of the two fractions.

In this case, the least common multiple of #3# and #5# is #15#, which means that you will have to multiply the first fraction by #1 = 3/3# and the second fraction by #1 = 5/5# to get

#(5x+6)/5 * 3/3 = (4x+10)/3 * 5/5#

#(3(5x+6))/15 = (5(4x+10))/15#

At this point, you know that the equation comes down to

#3 * (5x+6) = 5 * (4x + 10)#

Expand the parantheses and isolate #x# on one side of the equation to get

#15x + 18 = 20x + 50#

#15x - 20x = 50 - 18#

#-5x = 32 implies x= color(green)(-32/5)#

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