SOLVING EQUATION CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Example 6: tex2html_wrap_inline248




Either tex2html_wrap_inline250 or tex2html_wrap_inline252



Solve tex2html_wrap_inline254

eqnarray41




eqnarray55




eqnarray62




eqnarray70




Solve tex2html_wrap_inline252

eqnarray84




eqnarray98




eqnarray105




eqnarray113




The answers are 3.20567553681, -0.688434161172, 1.75320261515 and -2.33459796399. 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=1.70156211872 by substituting 1.70156211872 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 to the right side of the original equation after 1.70156211872 was substituted for x, the answer x=1.70156211872 is a solution to the original equation.




Check x= -0.688434161172 by substituting -0.688434161172 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 not equal to the right side of the original equation after -0.688434161172 is substituted for x, the answer x= -0.688434161172 is a not solution to the original equation.




Check x= 1.75320261515 by substituting 1.75320261515 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 to the right side of the original equation after 1.75320261515 was substituted for x, the answer x= 1.75320261515 is a solution to the original equation.




Check x=-2.33459796399 by substituting -2.33459796399 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 not equal to the right side of the original equation after -2.33459796399 was substituted for x, the answer x=-2.33459796399 is not a solution to the original equation. Since we rounded the solution, the check will not be exact.




The solutions are x=3.20567553681 and 1.75320261515.



You can also check your answer by graphing

tex2html_wrap_inline326
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 two x-intercepts on the graph are located at x=3.20567553681 and 1.75320261515. This verifies the two solutions by a graphical method.


If you would like to test yourself by working some problems similar to this example, clicks 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]

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 1999-2017 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