How do you solve #\frac { 2( 3w + 4) } { 5} = \frac { 2( 2w - 1) } { 3}#?

1 Answer
Jim G.
Nov 6, 2016

#w=17#

Explanation:

To eliminate the fractions, mutiply both sides of the equation by the lowest common multiple ( LCM ) of 5 and 3, which is 15.

#rArrcancel(15)^3xx(2(3w+4))/cancel(5)^1=cancel(15)^5xx(2(2w-1))/cancel(3)^1#

#rArr6(3w+4)=10(2w-1)larr" no fractions"#

distribute the brackets on both sides.

#18w+24=20w-10#

subtract 20w from both sides.

#18w-20w+24=cancel(20w)cancel(-20w)-10#

#rArr-2w+24=-10#

subtract 24 from both sides.

#-2wcancel(+24)cancel(-24)=-10-24#

#rArr-2w=-34#

To solve for w, divide both sides by - 2.

#(cancel(-2) w)/cancel(-2)=(-34)/(-2)#

#rArrw=17" is the solution"#

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