How do you solve #abs(2x+9) ≤ 3#?

Answer 1

#-6 le x le-3#

Because it has the absolute value sign, you can assume there are two equations: #2x+9le3# and #-(2x+9)le3#
Lets solve for the first one. #2xle-6# #xle-3#
Now onto the second one. #2x+9ge-3# #2xge-12# #xge-6#
Now combine the two answers. #xle-3# and #xge-6# for #-6lexle-3#
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Answer 2

(-6 \leq 2x + 9 \leq 6)
(-15 \leq 2x \leq -3)
(-7.5 \leq x \leq -1.5)

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Answer 3

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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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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