# How do you solve #6x - 5 < 6/x#?

To help you determine the intervals on which this quadratic function is smaller than zero, you need to first determine its root by using the quadratic formula

You can thus rewrite the quadratic as

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To solve (6x - 5 < \frac{6}{x}), follow these steps:

- Multiply both sides by (x) to clear the fraction: (6x^2 - 5x < 6).
- Rearrange the inequality: (6x^2 - 5x - 6 < 0).
- Factor the quadratic equation: ((2x - 3)(3x + 2) < 0).
- Determine the critical points by setting each factor equal to zero: (x = \frac{3}{2}) and (x = -\frac{2}{3}).
- Plot these critical points on a number line and test intervals.
- Determine the sign of each factor in each interval to find where the inequality holds true.
- The solution is the interval where the inequality holds true.

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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.

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.

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.

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