SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)

Note:


Solve for x in the following equation.

Problem 3.5d:

tex2html_wrap_inline166 tex2html_wrap_inline166



Answer:tex2html_wrap_inline166 tex2html_wrap_inline168



Solution:

Either tex2html_wrap_inline166 tex2html_wrap_inline170 tex2html_wrap_inline166 or tex2html_wrap_inline166 tex2html_wrap_inline172






Step 1:tex2html_wrap_inline166 Solve tex2html_wrap_inline174

eqnarray39


eqnarray46







Step 2:tex2html_wrap_inline166 Solve tex2html_wrap_inline172

eqnarray57


eqnarray64





There are four answers; tex2html_wrap_inline178 However all these answers may or may not be solutions. You must verify that your answers are the solutions to the original equation.







Step 4:tex2html_wrap_inline166 Check the solutions:

Check x=2.57603367 by substituting 2.57603367 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 we substitute the value 2.57603367 for x, then x=2.57603367 is not a solution.







Check the solution x = - 4.07603367 by substituting -4.07603367 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 we substitute the value -4.07603367 for x, then x=-4.07603367 is a solution.







Check the solution x=2.7413587 by substituting 2.7413587 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 we substitute the value 2.7413587 for x, then x=2.7413587 is not a solution.







Check the solution x=-0.8663587 by substituting x=-0.8663587 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 we substitute the value x=-0.8663587 for x, then x=-0.8663587 is a solution.







There are two solutions: tex2html_wrap_inline168






You can also verify these two real answers by graphing

eqnarray123

The graph is formed by subtracting the right side of the original equation from the left side of the original equation. Note that there are two x-intercepts at x=-4.07603367,x=-0.86635871. This verifies the solutions.



If you would like to go back to the problem page, 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 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 1999-2017 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