About this paper

Appears in:
Pages: 1933-1940
Publication year: 2018
ISBN: 978-84-697-9480-7
ISSN: 2340-1079
doi: 10.21125/inted.2018.0345

Conference name: 12th International Technology, Education and Development Conference
Dates: 5-7 March, 2018
Location: Valencia, Spain

FUNCTIONS AND LOGIC IN SOLVING EQUATIONS AND INEQUALITIES

S. Litvinov1, E. Litvinova2

1Pennsylvania State University - Hazleton (UNITED STATES)
2Bloomsburg University (UNITED STATES)
In order to justify a solution of an equation/inequality, one has to view this equation/inequality as a statement concerning the unknowns that is given in terms of suitable functions. The next step is to present a sequence of equivalent statements concerning the unknowns - that we call conjunction-disjunction complexes - such that the last statement describes the solution set of the equation/inequality. To ensure that the intermediate statements are indeed equivalent (or, in the case of solving an equation, each such statement is, at least, a consequence of the previous one), one needs to follow rules of logic and keep track of the domains of the functions involved. This talk is devoted to a discussion of general principles of solving equations/inequalities based on the notion of function combined with utilization of simple rules of logic. We then apply these principles to different types of equations/inequalities such as involving rational, irrational, logarithmic and other functions and provide concrete examples where such equations/inequalities are solved. Understanding the approach suggested in the paper allows to avoid many common mistakes that occur when solving complex equations/inequalities and systems of equations/inequalities. Presented material shall be of interest to high school/college instructors who teach algebra/pre-calculus courses.
@InProceedings{LITVINOV2018FUN,
author = {Litvinov, S. and Litvinova, E.},
title = {FUNCTIONS AND LOGIC IN SOLVING EQUATIONS AND INEQUALITIES},
series = {12th International Technology, Education and Development Conference},
booktitle = {INTED2018 Proceedings},
isbn = {978-84-697-9480-7},
issn = {2340-1079},
doi = {10.21125/inted.2018.0345},
url = {http://dx.doi.org/10.21125/inted.2018.0345},
publisher = {IATED},
location = {Valencia, Spain},
month = {5-7 March, 2018},
year = {2018},
pages = {1933-1940}}
TY - CONF
AU - S. Litvinov AU - E. Litvinova
TI - FUNCTIONS AND LOGIC IN SOLVING EQUATIONS AND INEQUALITIES
SN - 978-84-697-9480-7/2340-1079
DO - 10.21125/inted.2018.0345
PY - 2018
Y1 - 5-7 March, 2018
CI - Valencia, Spain
JO - 12th International Technology, Education and Development Conference
JA - INTED2018 Proceedings
SP - 1933
EP - 1940
ER -
S. Litvinov, E. Litvinova (2018) FUNCTIONS AND LOGIC IN SOLVING EQUATIONS AND INEQUALITIES, INTED2018 Proceedings, pp. 1933-1940.
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