How do you solve #abs(2x+9) ≤ 3#?
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(-6 \leq 2x + 9 \leq 6)
(-15 \leq 2x \leq -3)
(-7.5 \leq x \leq -1.5)
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To solve the inequality |2x + 9| ≤ 3, we'll consider two cases:
Case 1: 2x + 9 ≥ 0 Case 2: 2x + 9 < 0
For Case 1: 2x + 9 ≤ 3 Subtract 9 from both sides: 2x ≤ -6 Divide both sides by 2: x ≤ -3
For Case 2: -(2x + 9) ≤ 3 Distribute the negative sign: -2x - 9 ≤ 3 Add 9 to both sides: -2x ≤ 12 Divide both sides by -2 (remember to reverse the inequality because we're dividing by a negative number): x ≥ -6
Therefore, the solution to the inequality |2x + 9| ≤ 3 is -6 ≤ x ≤ -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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