Intervals On Number Line

[nycmath]

Precalculus
David Cohen
Edition 3
Chapter 1, Section 1.2

Show intervals on a number line.

58. | x - 1 | < 4

62. | x + 5 | > or = 2

[Eigenvalue]

58. |x-1|<4 means that the distance from x to 1 is less than 4
x-1>-4 and x-1<4
-4<x-1<4
-3<x<5

62. |x+5|[tex]\ge[/tex]2 means that the distance from x to negative 5 is greater than or equal to 2
x+5[tex]\ge[/tex]2 or x+5[tex]\le[/tex]-2
x[tex]\ge[/tex]-3 or x[tex]\le[/tex]-7

[Eigenvalue]

Generalized formulas:
|x-h|>c
x-h>c or x-h<-c
x>h+c or x<-(h+k)

|x-h|<c
x-h>-c and x-h<c
h-c<x<h+c

[nycmath]

58. |x-1|<4 means that the distance from x to 1 is less than 4
x-1>-4 and x-1<4
-4<x-1<4
-3<x<5

62. |x+5|[tex]\ge[/tex]2 means that the distance from x to negative 5 is greater than or equal to 2
x+5[tex]\ge[/tex]2 or x+5[tex]\le[/tex]-2
x[tex]\ge[/tex]-3 or x[tex]\le[/tex]-7

Thank you for your effort. Where's the number line?

[Eigenvalue]

The website is somehow not letting me post pictures from my phone. I will try it with my laptop

[nycmath]

The website is somehow not letting me post pictures from my phone. I will try it with my laptop

The number line picture requested is not only for me but for members to see and learn.