Number Line & Intervals (Part 2)

  • #1
mathdad
1,283
1
The set of real numbers satisfying the given inequality is one or more intervals on the number line. Show the intervals on a number line.

(A) |x - 4| < 4

(B) |x + 5| >= 2

For (A), I did the following:

-4 < x - 4 < 4

I now add 4 to each term.

0 < x < 8

On the number line, I would need to plot (0, 8). Is this correct?

For (B), we have the following:

|x + 5| >= 2

x + 5 < -2 or x + 5 >= 2

x =< -2 - 5 or x >= 2 - 5

x =< - 7 or x >= -3

I must plot [-infinity, -7] and [-3, infinity] on the number line. Is this right?
 
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  • #2
a)

I would read this as a distance formula, that is, all real numbers that are less than 4 units from 4, which as you stated is the interval .



b)

I would read this as all real numbers whose distance from is greater than or equal to 2, which as you stated is the interval .

 
  • #3
MarkFL said:
a)

I would read this as a distance formula, that is, all real numbers that are less than 4 units from 4, which as you stated is the interval .



b)

I would read this as all real numbers whose distance from is greater than or equal to 2, which as you stated is the interval .


Cool. Thanks.
 

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