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How do you solve #-5abs(x+13)+34<=9#?

Answer 1

Hazel Anglin

Solve# -5|x + 13| + 34 <= 9#

#5|x + 13| >= 34 - 9#

#|x + 13| >= 5#

Separate solving into 2 cases.

a.# (x + 13) > 5 -> x > 5 - 13 -> x >= - 8#

b.# - (x + 13) = - x - 13 > 5 --> x <= -13 - 5 -> x <= - 18# Graph

========|-18-----------------|-8=====|0=========

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Answer 2

Eli Assouline

To solve the inequality -5|𝑥+13|+34 ≤ 9, you would first subtract 34 from both sides to isolate the absolute value term. This gives you -5|𝑥+13| ≤ -25. Then, divide both sides by -5, remembering to reverse the inequality sign since you're dividing by a negative number. This yields |𝑥+13| ≥ 5. Now, you have two cases: 𝑥+13 ≥ 5 and 𝑥+13 ≤ -5. Solve each case separately to find the solutions. Subtracting 13 from both sides gives 𝑥 ≥ -8 and 𝑥 ≤ -18. Therefore, the solution set for the inequality is 𝑥 ≤ -18 or 𝑥 ≥ -8.

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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.

How do you solve #-5abs(x+13)+34&lt;=9#?

How do you solve #-5abs(x+13)+34<=9#?