How do you solve and write the following in interval notation: #|2x + 9 |>= 15#?

Answer 1

#x>=3# or #x<=-12#; Expressed in interval notation: #(-oo, -12]uu[3,oo)#

#|2x+9|>=15 :. 2x+9>=15 or 2x>=6 or x>=3# OR #|2x+9|>=15 :. 2x+9<=-15 or 2x<=-24 or x<=-12# Expressed in interval notation: #(-oo, -12]uu[3,oo)#[Ans]
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Answer 2

To solve the absolute value inequality |2x + 9| ≥ 15 and write the solution in interval notation:

  1. First, isolate the absolute value expression by considering two cases: when the expression inside the absolute value is positive and when it is negative.

  2. For the case when 2x + 9 is positive: 2x + 9 ≥ 15 Solve for x: x ≥ 3

  3. For the case when 2x + 9 is negative: -(2x + 9) ≥ 15 Solve for x: x ≤ -12

  4. Combine the solutions from both cases: x ≤ -12 or x ≥ 3

  5. Write the solution in interval notation: (-∞, -12] ∪ [3, ∞)

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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.

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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