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

1 Answer
Fir3hawk
May 21, 2017

x<56/19x<5619

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))/23(6−x)2: We multiply this by 5/555
(3(6-x))/2*5/53(6−x)2⋅55 = (5(18-3x))/(2*5)*5/55(18−3x)2⋅5⋅55 = (90-15x)/(10)90−15x10

-3−3: We multiply this by 10/101010
-3/1*10/10 = -30/10−31⋅1010=−3010

(2(1+x))/52(1+x)5: We multiply this by 2/222
(2(1+x))/5*2/2 = (4(1+x))/(5*2) = (4+4x)/102(1+x)5⋅22=4(1+x)5⋅2=4+4x10

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)/1090−15x10−3010>4+4x10

=> (90-15x)-30 > 4+4x(90−15x)−30>4+4x
=> 60-15x > 4+4x60−15x>4+4x
=> -19x > -56−19x>−56
=> x<56/19 x<5619

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