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How do you solve and write the following in interval notation: #-2x<3-x<=8#?

Answer 1

Julia Adams

#x in ]-3;+oo[#

Let's write and solve the equivalent:

#-2x<3-x and 3-x<=8#

#2x-x> -3 and x>=3-8#

#x > -3 and x>=-5#

that's

#x> -3#

or, in interval notation:

#x in ]-3;+oo[#

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Answer 2

Abigail Allen

To solve and write the inequality -2x < 3 - x ≤ 8 in interval notation, you first need to solve it step by step:

Start by solving -2x < 3 - x: -2x < 3 - x -2x + x < 3 -x < 3
Divide both sides by -1, but remember to reverse the inequality sign: x > -3
Now solve 3 - x ≤ 8: 3 - x ≤ 8 -x ≤ 8 - 3 -x ≤ 5
Divide both sides by -1, but remember to reverse the inequality sign: x ≥ -5

So, the solution is -3 < x ≤ 8.

In interval notation, this can be written as: (-3, 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 and write the following in interval notation: #-2x&lt;3-x&lt;=8#?

How do you solve and write the following in interval notation: #-2x<3-x<=8#?