How do you solve #\frac { 2} { 3} x = - \frac { 1} { 2}#?

1 Answer
Jim G.
Dec 5, 2016

#x=-3/4#

Explanation:

Note that the left side of the equation can be written.

#(2x)/3" as "2/3xx x/1=(2xxx)/(3xx1)=(2x)/3 #

We want to ' eliminate' the fractions in this equation.

To do this we multiply #color(blue)"both sides"# by the #color(blue)"lowest common multiple "# of 3 and 2, that is 6 and
#color(blue)"cancel"#

#cancel(6)^2/1xx(2x)/cancel(3)^1=cancel(6)^3/1xx-1/cancel(2)^1#

#rArr(2xx2x)/(1xx1)=(3xx-1)/(1xx1)#

#rArr4x=-3#

Now to solve for x, divide both sides by 4

#(cancel(4) x)/cancel(4)=-3/4#

#rArrx=-3/4" is the solution"#

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