How do you solve #\frac { 9x } { 2} + \frac { 3} { 4} = - \frac { 33} { 4}#?

1 Answer
Jim G.
Mar 11, 2017

#x=-2#

Explanation:

To eliminate the fractions in the equation multiply ALL terms on both sides by the #color(blue)"lowest common multiple"# ( LCM) of 2 and 4, the denominators of the fractions.

The LCM of 2 and 4 is 4

#(cancel(4)^2 xx(9x)/cancel(2)^1)+(cancel(4)^1 xx3/cancel(4)^1)=(cancel(4)^1xx-33/cancel(4)^1)#

#rArr18x+3=-33larrcolor(red)" no fractions"#

subtract 3 from both sides.

#18xcancel(+3)cancel(-3)=-33-3#

#rArr18x=-36#

divide both sides by 18

#(cancel(18) x)/cancel(18)=(-36)/18#

#rArrx=-2#

#color(blue)"As a check"#

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

#"left side "=((9xx-2))/2+3/4=-9+3/4=-8 1/4=-33/4#

#rArrx=-2" is the solution"#

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