How do you solve and write the following in interval notation: #4<1/x<= 1 #?
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We are doing case work to solve this inequality:
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To solve and write the inequality 4 < 1/x ≤ 1 in interval notation:
 Find the critical points where the expression 1/x equals zero or is undefined.
 Solve the inequalities individually for each interval created by the critical points.
 Write the solution using interval notation.
The critical point is x = 0, where 1/x is undefined.

For x > 0: Solve 1/x ≤ 1.
 Multiply both sides by x (since x is positive): 1 ≤ x.
 So, the solution for x > 0 is x ∈ [1, ∞).

For x < 0: Solve 4 < 1/x.
 Multiply both sides by x (since x is negative, flip the inequality): x < 4.
 Divide both sides by 1 (flip the inequality): x > 4.
 So, the solution for x < 0 is x ∈ (∞, 4).
Combine the solutions for both intervals:
 The interval notation for the solution is: x ∈ (∞, 4) ∪ [1, ∞).
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When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
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