Absolute Value Equations
Absolute value equations can be tricky if you’re not careful.
These equations can have as many as two solutions!
So how do you solve them correctly? Just follow these steps:
1. Rewrite the main equation into two equations.
One will be positive and the other will be negative.
Example: |x|= 5 is rewritten as x = 5 and x = - 5
2. Solve these two new equations as you
would a regular algebra equation.
Example: x = 5 and x = -5
3. Plug each solution back into the original
equation and check to see if each one works.
Example: |5| = 5 is correct.
|-5| = 5 is also correct
This equation has two solutions.
Of course, not all absolute value equations are as simple as |x|= 5.
The variable x is not always alone “inside” the absolute value.
With these kinds of equations, you still follow the basic steps to solve.
1. Rewrite the main equation.
Example: |x - 2|= 14 is rewritten as x - 2 = 14 and x - 2 = -14.
2. Solve the new equations.
Example: x - 2 = 14 means x = 16
x - 2= -14 means x = -12
3. Plug each answer back into the equation.
Example: |(16) - 2| = 14 means |14|= 14
|(-12) - 2| = 14 means |-14|=14
Both solutions are correct.
By using these basic steps,
you can solve any absolute value equation!
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