SOLUTION: Solve the inequality. Express your answer using set notation and interval notation. Graph the solution set.
(2x - 1)^(-1) > 0
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-> SOLUTION: Solve the inequality. Express your answer using set notation and interval notation. Graph the solution set.
(2x - 1)^(-1) > 0
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Your inequality is equivalent to this one
> 0.
The fraction is positive if and only if the denominator is positive
2x - 1 > 0.
Add 1 to both sides. You will get an equivalent inequality
2x > 1.
Divide both sides by 2. You will get an equivalent inequality
x > 1/2.
It is your ANSWER. In the interval form (1/2,oo).
In the graph form
----------|-----------o=============|========================|====>
0 1/2 1 2
As mentioned by the other tutor, 1/(2x-1) is positive if and only if 2x-1 > 0.
That solves to x > 1/2
A visual way to demonstrate this is to use a graphing tool like GeoGebra or Desmos to plot the graph of y = 1/(2x-1)
The vertical asymptote is x = 1/2 since this x value makes the denominator 2x-1 to be zero. Recall that dividing by zero is not allowed.
The portion of the curve to the right of x = 1/2 is entirely above the x axis.
So we visually demonstrate the answer as an inequality is x > 1/2
You can verify this using a table of values.
The answer in interval notation is (1/2, infinity)
Replace the word "infinity" with the symbol if needed.
The graph on a number line will involve an open hole at 1/2 and shading to the right. The open hole indicates "do not include this endpoint".
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