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How do you solve and write the following in interval notation: #4 ≤ 3 − x <8#?

Answer 1

Eli Assouline

#(-5,-1]#

#"isolate x in the middle interval by subtracting 3 from all 3"# #"intervals"#

#4-3<=3-3-x<8-3#

#rArr1<=-x<5#

#"multiply all 3 intervals by - 1 remembering to reverse the"# #"inequality signs"#

#rArr-1>=x> -5larrcolor(red)" reverse signs"#

#"in interval notation as "(-5,-1]#

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Answer 2

Julia Adams

To solve and write the inequality (4 \leq 3 - x < 8) in interval notation:

Subtract 3 from each part of the inequality: (1 \leq -x < 5)
Multiply each part by -1 (which reverses the inequality signs): (-1 \geq x > -5)
Write the result in interval notation: ([-1, -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: #4 ≤ 3 − x &lt;8#?

How do you solve and write the following in interval notation: #4 ≤ 3 − x <8#?