Positive and Negative Integers

Positive integers are all the natural numbers greater than zero:

1, 2, 3, 4, 5, ...

Negative integers are all the opposites of these natural numbers:

-1, -2, -3, -4, -5, …

We do not consider zero to be a positive or negative number. So, the opposite of 0 is 0. For each positive integer, there is a negative integer, and these integers are called opposites.

For example, -3 is the opposite of 3, -21 is the opposite of 21, and 8 is the opposite of -8.

If an integer is greater than zero, we say that its sign is positive.

If an integer is less than zero, we say that its sign is negative.

Absolute Value

| a + b | < c means – c < a + b < c

Problem: |x + 3| < 7

Use the formula to solve:

-7 < x + 3 < 7

Subtract 3 from each section:

-7 < x + 3 < 7

-3         -3   -3

-10 <   x   < 4

  O-------------------------------------------------------O

_|__|__|__|__|__|__|__|__|__|__|__|__|__|__|_

-10-9 -8  -7  -6  -5  -4  -3 -2  -1   0   1   2   3   4