How do you solve and write the following in interval notation: #| -3x | + 2 ≤ 8#?
See the entire solution process below:
The absolute value function takes any positive or negative term and transforms it to its positive form. Therefore, you must solve the term within the absolute value function for both its positive and negative equivalent:
Or
Or, in interval notation:
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To solve | -3x | + 2 ≤ 8 in interval notation, you would follow these steps:
- Subtract 2 from both sides: | -3x | ≤ 6
- Divide both sides by 3: | x | ≤ 2
- Split into two cases: x ≤ 2 and x ≥ -2
- Combine the two cases: -2 ≤ x ≤ 2
So, the solution in interval notation is [-2, 2].
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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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