Question 1199342: Solve the inequality. Express your answers using set notation or interval notation. Graph the solution set.
0 < (2x - 4)^(-1) < 1/2
Let me see.
Let (2x - 4)^(-1) be 1/(2x - 4).
We now have this:
0 < 1/(2x - 4) < 1/2
Stuck here....
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the answer will be x > 3
here's my reasoning.
your inequality is 0 < (2x-4)^-1<1/2
that becomes:
0 < 1/(2x-4) < 1/2
multiply all sides of the inequality by (2x-4) to get:
0 < 1 < 1/2 * (2x-4)
simplify to get:
0 < 1 < (x-2)
add 2 to all sides of the inequality to get:
2 < 3 < x
is x > 3, then x has to be > 2, so reduce the inequality to:
3 < x
solve for x to get:
x > 3
to see if this is a good solution, replace x with something greater than 3, like 4.
your equation becomes 0 < 1/(8-2) < 1/2
simplify to get:
0 < 1/6 < 1/2
this is a true statement because 0 < 1/6 and 1/6 < 1/2.
your solution is x > 3 as far as i can tell.
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
I will continue, starting from the point where you stop.
So, we should solve this inequality
0 <  < 
Thus, we have, actually, two inequalities
(a) 0 < and (b) < .
From (a), we have that 2x-4 is positive
2x - 4 > 0,
which implies 2x > 4; hence, x > 2 (after diving both sides by 2 in the previous inequality).
From (b), we have 2 < 2x-4 (after cross-multiplying of (b)).
It implies 2+4 < 2x, or 6 < 2x; hence, x > 3.
Of two inequalities, x > 2 and x > 3, their solution is x > 3.
ANSWER. The solution to given compound inequality is the interval (3,oo), or {x | x > 3}.
Solved.
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