SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 2:

tex2html_wrap_inline112




Step 1:The absolute value is already isolated.

Since tex2html_wrap_inline114 and tex2html_wrap_inline116 , 5x+7=3 or 5x+7=-3





Step 2:Set the quantity within the absolute value notation to tex2html_wrap_inline122



eqnarray32




Step 3:Solve for x in the equation 5x+7=3



eqnarray35

Solve for x in the equation 5x+7=-3.

eqnarray40

The answers are tex2html_wrap_inline128 and -2.





Step 4: Check the solutions because answers are not always valid solutions to the equation.





Check the solution x = tex2html_wrap_inline128 by substituting tex2html_wrap_inline128 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 after we substituted the value tex2html_wrap_inline128 for, the solution tex2html_wrap_inline142 is valid




Check the solution x = -2 by substituting -2 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 after we substituted the value -2 for, the solution x=-2 is valid





You can also check your answer by graphing



displaymath100



(the left side of the original equation minus the right side of the original equation). You will note that the two x-intercepts on the graph are located at tex2html_wrap_inline128 and -2. this verifies our solutions graphically.



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 Problems

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 Algebra]

S.O.S MATHematics home page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Author:Nancy Marcus

Copyright © 1999-2024 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour