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How to Graph Absolute Value Inequalities With Two Variables

A number line has 0 at its center with negative numbers extending to the left and positive numbers to the right. A positive number and its negative equivalent, such as 5 and -5, are both 5 spaces from 0. In some instances, distance from 0 is more important than the sign of the number. This is when the absolute value symbol is used in equations. Absolute value, represented with two vertical bars, ensures that whatever is within the bars results in a positive number. For example, |-3| = 3. But when there's an operation to be performed within the bars, such as |-6 + x|, the positive and negative values for "x" need to be solved because they result in different answers within the bars.

Instructions

- 1
  Graph the absolute value function y = |x + 4| by first creating a t-chart with the left column labeled "x" and the right labeled "y = |x + 4|." Choose six values for the "x," including three negative numbers and three positive to get a full idea of the shape of the graph. For example, use -4, -2, -1 and 1, 2 and 4. Solve for the y-values and the graphical points.
- 2
  Solve for -4 -- |-4 + 4| = 0 or point (-4, 0). Solve for -2 -- |-2 + 4| = 2 or point (-2, 1). Solve for -1 -- |-1 + 4| = 3 or point (-1, 3). Solve for 1 -- |1 + 4| = 5 or point (1, 5). Solve for 2 -- |2 + 4| = 6 or point (2, 6). Solve for 4 -- |4 + 4| = 8 or point (4, 8).
- 3
  Graph the points then draw a connecting line with arrows drawn on each end to represent continuation.

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