How do you solve #-1/2p + 1/6p = -2/3#?

1 Answer
Jim G.
Jan 22, 2017

#p=2#

Explanation:

To 'eliminate' the fractions, multiply ALL terms on both sides of the equation by the #color(blue)"lowest common multiple"# (LCM) of the denominators 2, 6 and 3

The LCM of 2, 6 and 3 is 6

#rArr( -cancel(6)^3xxp/cancel(2)^1)+(cancel(6)^1xxp/cancel(6)^1)=(-cancel(6)^2xx2/cancel(3)^1)#

#rArr-3p+p=-4larr" no fractions"#

simplifying.

#-2p=-4#

To solve for p, divide both sides by - 2

#(cancel(-2) p)/cancel(-2)=(-4)/(-2)#

#rArrp=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.

#p=2to(-1/2xx2)+(1/6xx2)=-1+1/3=-2/3#

#rArrp=2" is the solution"#

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