How do you solve and write the following in interval notation: #2x - 4< 4# or# x + 5 ≤ 2 - 2x#?

Answer 1
  1. #x<4# and in interval notation # x in(-oo,4)#
  2. #x<=-1# and in interval notation #x in(-oo,-1]#

Lets take the first example.

#2x-4<4#

This is an inequality. Inequalities are usually solved like regular equations.

Lets add #4# to both sides of the equation.
#2x-4+color(red)4<4+color(red)4#
#2x
Divide both sides by #2#
#(2x)/color(red)2<8/color(red)2#
#x<4#
This inequality means that the value of #x# has to be less than #4# to satisfy the inequality.
In interval notation it will be written as # x in(-oo,4)# because the value of #x# can be any number between #-oo# and #4# but cannot be #-oo# or #4# hence we use this ( ) bracket.
Similarly when we simplify #x+5<=2-2x# we get #x<=-1#
So here the interval notation is #x in(-oo,-1]# because #x# can be any number between #-oo# and #-1# and can be #-1# but cannot be #-oo# hence this ( ] bracket.
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Answer 2

The solution to the inequality 2x - 4 < 4 or x + 5 ≤ 2 - 2x is x < 4 or x ≥ -1. In interval notation, this is written as (-∞, 4) ∪ [-1, ∞).

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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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