#### SOLVING EQUATION CONTAINING ABSOLUTE VALUE(S)

Note:

**Solve for x in the following equation.**

Example 4:

**
**

Isolate the absolute value term by subtracting 2x from both sides of the
equation.

Either or

Solve **
**

Solve **
**

The answers are 1.06811457479, -0.468114574787, 2.04880884817 and
-0.04880884817. These answers may or may not be solutions to the original
equation. You must verify each of the answers.

Check the solutions:

Check the answer *x* = 1.06811457479 by substituting 1.06811457479 in the
original equation for x. If the left side of the equation equals the right
side of the equation after the substitution, you have found the correct
answer.

- Left Side:

- Right Side:

Since the left side of the original equation is equal to the right side of
the original equation after 1.06811457479 was substituted for x, the
answer *x*=1.06811457479 is a solution to the original equation.

Check *x*=-0.468114574787 by substituting -0.468114574787 in the original
equation for x. If the left side of the equation equals the right side of
the equation after the substitution, you have found the correct
answer.

- Left Side:

- Right Side:

Since the left side of the original equation is equal to the right side of
the original equation after -0.468114574787 is substituted for x, the
answer *x*=-0.468114574787 is a solution to the original equation.

Check *x*=2.04880884817 by substituting 2.04880884817 in the original
equation for x. If the left side of the equation equals the right side of
the equation after the substitution, you have found the correct
answer.

Since the left side of the original equation is equal not to the right side
of the original equation after 2.04880884817 was substituted for x, the
answer *x*=2.04880884817 is not a solution to the original equation.

Check *x*=-0.04880884817 by substituting -0.04880884817 in the original
equation for x. If the left side of the equation equals the right side of
the equation after the substitution, you have found the correct
answer.

- Left Side:

- Right Side:

Since the left side of the original equation is equal to the right side of
the original equation after -0.04880884817 was substituted for x, the
answer *x*=-0.04880884817 is a solution to the original equation. Since we
rounded the solution, the check will not be exact.

The solutions are *x*=1.06811457479,-0.468114574787, and -0.04880884817.

You can also check your answer by graphing

The graph was formed by subtracting the right side of the
original equation from the left side of the original equation. You will note
that there are three x-intercepts on the graph are located at
*x*=1.06811457479,-0.468114574787, and -0.04880884817. This verifies the
three solutions by a graphical method.

If you would like to work another example, click on
example.
If you would like to test yourself by working some problems similar to
this example, click on problem.

If you would like to go back to the equation table of contents, click on contents.

**
[Algebra]
[Trigonometry]
****
[Geometry]
[Differential
Equations]
****
[Calculus]
[Complex Variables]
[Matrix]**

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