How do you solve compound inequalities #4x + 7 < 11 or 1 – x ≤ -2#?
Initially treat the two inequalities separately
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To solve compound inequalities like (4x + 7 < 11) or (1 - x \leq -2), we solve each inequality separately and then combine their solutions.
For the first inequality (4x + 7 < 11): [4x + 7 < 11] [4x < 11 - 7] [4x < 4] [x < 1]
For the second inequality (1 - x \leq -2): [1 - x \leq -2] [-x \leq -3] Since we multiplied by -1, we flip the inequality sign: [x \geq 3]
Combining the solutions, we have (x < 1) or (x \geq 3).
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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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