How do you solve 3(6−x)2−3>2(1+x)5?

1 Answer
Fir3hawk
May 21, 2017

x<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)2: We multiply this by 55
3(6−x)2⋅55 = 5(18−3x)2⋅5⋅55 = 90−15x10

−3: We multiply this by 1010
−31⋅1010=−3010

2(1+x)5: We multiply this by 22
2(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:

90−15x10−3010>4+4x10

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

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