Real numbers can be visualized using a number line. Number lines are helpful for picturing a number of algebra concepts, including opposite numbers, operations of real numbers, and inequalities.
Number Line: A straight line where every point on the line represents a real number
Opposite Numbers: Two numbers that are the same distance from zero but on opposite sides of the number line.
Absolute Value: The absolute value of a number is the distance of that number from 0.
All real numbers can be drawn on a number line. A number line plots the greatest number to the farthest right, and the least to the farthest left.
The number line above is divided into intervals of 1, so the numbers on the line increase by +1 from left to right. A number line can be divided into as many sub-intervals as you need. To plot \(\frac{2}{3}\) on the number line, you can have sub-intervals of \(\frac{2}{3}\)
A number line represents all real numbers (that’s an infinite amount of numbers)!
Opposite numbers are on opposite sides of 0 and are the same distance away from zero.
The absolute value of a number is its distance from zero.
To add numbers on a number line, start on the first number in the expression. If you are adding a positive number, then move to the right by the number of units equal to the next number in the expression.
Example:\( -2 + 3\)
To subtract numbers on a number line, move left instead of right. Subtracting a number is like adding a negative number.
Example: \(2 - 3 = 2 + (-3)\)
If a number is negative, move left, and if a number is positive, move right.
Inequalities in one variable can be shown on a number line.
If we want to show all the values of x that is greater than some number a, we are looking for all the numbers of x that will make x > a true. The number line would look like:
If we want to show x ≥ a, then we would want to include a. If x=a, then the inequality would still be true.
Showing less than (<) or less than and equal (≤) is similar, except the arrow would now point to the left.