How do you solve #\frac { 3( 6- x ) } { 2} - 3> \frac { 2( 1+ x ) } { 5}#?

1 Answer
Fir3hawk
May 21, 2017

#x<56/19#

Explanation:

First, to make life simple, we make sure all three terms have the same denominator. The least common denominator of this equation, as the current denominators are 1, 2, and 5.

#(3(6-x))/2#: We multiply this by #5/5#
#(3(6-x))/2*5/5# = #(5(18-3x))/(2*5)*5/5# = #(90-15x)/(10)#

#-3#: We multiply this by #10/10#
#-3/1*10/10 = -30/10#

#(2(1+x))/5#: We multiply this by #2/2#
#(2(1+x))/5*2/2 = (4(1+x))/(5*2) = (4+4x)/10#

Now, we combine and simplify. The denominators all cancel out through cross multiplication, so we are left with a simple inequality to solve:

#(90-15x)/(10) -30/10 > (4+4x)/10#

=> #(90-15x)-30 > 4+4x#
=> #60-15x > 4+4x#
=> #-19x > -56#
=> #x<56/19 #

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