SOLUTION: How to solve for x? a)(4x+2)^-1 < 0 b)0 < (2x-4)^-1 < 1/2

Algebra ->  Inequalities -> SOLUTION: How to solve for x? a)(4x+2)^-1 < 0 b)0 < (2x-4)^-1 < 1/2      Log On


   



Question 342197: How to solve for x?
a)(4x+2)^-1 < 0
b)0 < (2x-4)^-1 < 1/2

Answer by Edwin McCravy(20066) About Me  (Show Source):
You can put this solution on YOUR website!

a)
%284x%2B2%29%5E%28-1%29+%3C+0
1%2F%284x%2B2%29+%3C+0

That is only true if the denominator is negative:

4x%2B2+%3C+0

4x+%3C+-2

x%3C-2%2F4

x%3C-1%2F2

--------------------

b)

0+%3C+%282x-4%29%5E%28-1%29+%3C+1%2F2

0+%3C+1%2F%282x-4%29+%3C+1%2F2

We must requre that the denominator %282x-4%29 be positive,
so that we can multiple through by it without changing the order
of the inequality:

This requirement is 

2x-4%3E0
2x%3E4
x%3E2

0+%3C+1%2F%282x-4%29+%3C+1%2F2

0+%3C+1%2F%282%28x-2%29%29+%3C+1%2F2

With this requirement, we multiply through by the LCD = 2%28x-2%29

0+%3C+1+%3C+x-2

1+%3C+x-2

3+%3C+x

which is the same as 

x+%3E+3

which is consistent with the requirement x%3E2

so the solution is 

x%3E3

Edwin