How do you solve the inequality #x - 2 ≥ 2x + 1# or #-10> -2x - 2# ?
The solution for the first inequality is
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To solve the inequality (x - 2 \geq 2x + 1) or (-10 > -2x - 2), we'll solve each inequality separately and then combine the solutions.
For (x - 2 \geq 2x + 1):
(x - 2 \geq 2x + 1)
(x - 2x \geq 1 + 2)
(-x \geq 3)
Dividing both sides by -1, remember to flip the inequality sign:
(x \leq -3)
For (-10 > -2x - 2):
(-10 > -2x - 2)
Add 2 to both sides:
(-8 > -2x)
Divide both sides by -2, remember to flip the inequality sign:
(4 < x)
Combining the solutions:
(x \leq -3) or (4 < x)
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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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