Solving Absolute Value Equations

Tutoring on Solving Absolute Value Equations

Learning Objectives:

Understand to Solve Absolute Value Equation and Absolute Value Inequalities.

Solving Absolute Value Equations

A number's Absolute value is its distance from zero on the number line.  As we know a distance is always going to be positive, so when we transition to an absolute value equation, we can think of what numbers absolute values have. The Absolute Value Principle for equations is, for any positive number c and any algebraic expression x:

1.     The solutions of x = c, are those numbers that satisfy x = -c or x = c.

2.    The equation x = 0, is equivalent to the equation x = 0.

3.    The equation x = -c has no solutions.

 Here are the steps we are going to take to solve absolute value of equations:

1.    Isolate the absolute value.

2.   Set up and solve two equations based upon the absolute value principle.

3.    Lastly we will check answers.



Hook Questions


1.    What is the value of x in x = 5 ?

2.    Can you solve x = - 5 ?

3.    What is the difference between x = 0 and x = 0 ?


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