What are the intervals on the number line for | x + 5 | ≥ 2?

[mathdad]

The set of real numbers satisfying the given inequality is one or more intervals on the number line. Show each interval on the number line.

1. | x - 1 | < or = 1/2

Solution:

-1/2 < or = x - 1 < or = 1/2

(-1/2) + 1 < or = x < or = (1/2) + 1

1/2 < or = x < or = 3/2

----[1/2-------3/2]----

Correct?

2. | x + 5 | ≥ 2

Solution:

This question says that x is at least two units away from 5 on the number line.

x + 5 ≥ 2

x ≥ 2 - 5

x ≥ - 3

or

x + 5 ≤ -2

x ≤ - 2 - 5

x ≤ - 7

<---- -7]------[-3---->

Correct?

 

[Greg]

Both are correct.

 

[mathdad]

It surely feels good to be right.