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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