How do you solve #|-3x + 9| <24#?
See a solution process below:
The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
Or
Or, in interval notation:
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To solve the inequality (|-3x + 9| < 24), you can follow these steps:
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Split the inequality into two cases: a) (-3x + 9 < 24) b) (-3x + 9 > -24)
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Solve each case separately for (x).
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For case a), add 9 to both sides and divide by -3: (-3x < 24 - 9) (-3x < 15) Divide both sides by -3 (reverse the inequality since dividing by a negative number): (x > \frac{15}{-3}) (x > -5)
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For case b), subtract 9 from both sides and divide by -3: (-3x > -24 - 9) (-3x > -33) Divide both sides by -3 (reverse the inequality since dividing by a negative number): (x < \frac{-33}{-3}) (x < 11)
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Combine the solutions from both cases: (x) lies between -5 and 11: (-5 < x < 11)
So, the solution to the inequality (|-3x + 9| < 24) is (-5 < x < 11).
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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.
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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