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How do you solve and write the following in interval notation: # 1 /x <4#?

Answer 1

#(\frac{1}{4},\infty)#

Solve the inequality #4x>1# #x>\frac{1}{4}#

Since the value #x=\frac{1}{4}# is not a solution we use an open bracket. There is no upper limit so we use #infty# as the upper limit to get #(\frac{1}{4},\infty)#.

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Answer 2

Jameson Allen

To solve the inequality ( \frac{1}{x} < 4 ) and write it in interval notation, we follow these steps:

Determine the domain: Since we cannot divide by zero, ( x ) cannot equal zero.
Solve the inequality: ( \frac{1}{x} < 4 ) ( 1 < 4x ) ( \frac{1}{4} < x )
Write the solution in interval notation: ( x ) belongs to the interval ( \left( \frac{1}{4}, \infty \right) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve and write the following in interval notation: # 1 /x &lt;4#?

How do you solve and write the following in interval notation: # 1 /x <4#?