A line that holds every number
Algebra is built on numbers, so we start by giving numbers a home. The number line is a straight line with a marked 0 in the middle. To the right we place the counting numbers 1, 2, 3, …; adding 0 gives the whole numbers. To the left of zero we place their mirror images −1, −2, −3, …. Together the whole numbers and these negatives form the integers. Every integer sits at its own point, and the further right a number is, the larger it is.
Because the line is ordered, we can compare any two numbers with an inequality symbol. We write −3 < 1 (read “negative three is less than one”) precisely because −3 lies to the left of 1. This left-to-right order relation is the same idea you will lean on later when solving inequalities — it never changes.
Distance from zero: absolute value
The absolute value of a number is its distance from zero, ignoring direction. We write it with bars: |−4| = 4 and |4| = 4, because both points sit four steps from zero. Distance is never negative, so an absolute value is always 0 or positive. This single idea — strip the sign, keep the size — quietly underlies the rules for adding signed numbers in the next guide.
Reading the number line -4 -3 -2 -1 0 1 2 3 4 | | | | | | | | | Order: -3 < -1 < 0 < 2 < 4 (left is smaller) Sign: -3 is negative, 4 is positive, 0 has no sign Distance: |-3| = 3 |4| = 4 |0| = 0