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How do you solve and write the following in interval notation: #abs(5r + 2)< 18#?

Answer 1

#r<16/5 and r> -4# In interval notation: #(-4,16/5)#

#|5r+2| <18 :. 5r+2 <18 and 5r+2 > -18 or 5r<16 and 5r > -20 or r<16/5 and r > -4 :. -4 < r <16/5# In interval notation: #(-4,16/5)#[Ans]

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Answer 2

Genesis Allen

To solve the inequality abs(5r + 2) < 18 and write it in interval notation, you first need to isolate the absolute value expression and then consider the two cases: when the expression inside the absolute value is positive and when it's negative.

Case 1: 5r + 2 ≥ 0 Solve for r: 5r + 2 < 18 5r < 16 r < 16/5
Case 2: 5r + 2 < 0 Solve for r: -(5r + 2) < 18 -5r - 2 < 18 -5r < 20 r > -4

Combining both cases: -4 < r < 16/5

In interval notation, this solution is represented as (-4, 16/5).

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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 and write the following in interval notation: #abs(5r + 2)&lt; 18#?

How do you solve and write the following in interval notation: #abs(5r + 2)< 18#?