How do you solve #20/x=-5/2#?

2 Answers
smendyka
Dec 5, 2016

#x = -8#

Explanation:

First, you need to multiply each side by a common denominator to eliminate the fractions and keep the equation balanced. In this case the common denominator is #2x#:

#((2x)*20)/x = -(2x*-5)/2#

#((2cancel(x))*20)/cancel(x) = -(cancel(2)x*5)/cancel(2)#

#2*20 = -5x#

#-5x = 40#

Now we can solve for #x# while keeping the equation balanced:

#(-5x)/-5 = 40/(-5)#

#(cancel(-5)x)/cancel(-5) = -8#

#x = -8#

Jim G.
Dec 5, 2016

#x=-8#

Explanation:

When we have a fraction equal to another fraction, we can solve using the method of #color(blue)"cross-multiplication"#

The negative sign on the right side must be attached to either the 5 or the 2 but NOT BOTH. as this would give a positive result. I'm attaching it to the 2.

#rArrcolor(blue)(20)/color(red)(x)=color(red)(5)/color(blue)(-2)#

To cross-multiply, multiply the terms in #color(red)"red"# and the terms in #color(blue)"blue"# and equate them.

#rArrcolor(red)(5x)=(color(blue)(20)xxcolor(blue)(-2))#

#rArr5x=-40#

To solve for x, divide both sides by 5

#(cancel(5) x)/cancel(5)=(-40)/5#

#rArrx=-8" is the solution"#

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