Solving Absolute Value Equations
The absolute value of a real number x is defined by the following:
x = | x if x ≥ | 0 |
| 0 |
If n is a positive number, there are two solutions to the equation f (x) = n because there are exactly two numbers with the absolute value equal to n: n and
Example
Solve an absolute value equation 5 - 4x = 6
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1Enter y = 5 - 4x for Y1. Enter y = 6 for Y2.
Y= MATH B * 1 * 5 — 4
X//T/n ENTER * 6
2View the graph.
GRAPH
3Find the points of intersection of the two graphs and solve.
2nd F CALC 2 *
2nd F CALC 2 *
There are two points of in- tersection of the absolute value graph and the hori- zontal line y = 6.
The solution to the equation 5 - 4x= 6 consists of the two values
The