How do you solve #\frac { c - 9} { 4} = \frac { c - 5} { 2}#?

2 Answers
Jim G.
Mar 11, 2018

#c=1#

Explanation:

#"multiply both sides by the "color(blue)"lowest common multiple of 4 and 2"#

#"the lowest common multiple of 4 and 2 is 4"#

#cancel(4)^1xx(c-9)/cancel(4)^1=cancel(4)^2xx(c-5)/cancel(2)^1#

#rArrc-9=2(c-5)larrcolor(blue)"distribute"#

#c-9=2c-10#

#"subtract 2c from both sides"#

#c-2c-9=cancel(2c)cancel(-2c)-10#

#rArr-c-9=-10#

#"add 9 to both sides"#

#-c cancel(-9)cancel(+9)=-10+9#

#rArr-c=-1#

#"multiply both sides by "-1#

#rArrc=1" is the solution"#

Barney V.
Mar 11, 2018

#c=1#

Explanation:

#(c-9)/4=(c-5)/2#

With cross multiplication:-

#:.2(c-9)=4(c-5)#

#:.2c-18=4c-20#

#:.2c-4c=-20+18#

#:.-2c=-2#

#:.-c=-2/2#

#:.-c=-1#

multiply L.H.S and R.H.S. by# -1#

#:.-1xx-c=-1xx-1#

#:.c=1#

~~~~~~~~~~~~
check by substituting # x=1#

#:.((1)-9)/4=((1)-5)/2#

#:.cancel(-8)^-2/cancel 4^1=cancel(-4)^-2/cancel2^1#

#:.-2/1=-2/1#

#:.-2=-2#

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