Intermediate
Algebra Chapter 2
Equations, Inequalities and Problem Solving
| Worked out examples | Worked out examples | |
| Worked out examples |
Supplement to Section 2.2
1. Understanding
the problem usually requires that you know the vocabulary and some basic facts
about the field of application from which the problem arises.
If the problem comes from an engineering field, you must know something about
that engineering field.
If the problem comes from a medical field, you must know something about that
medical field.
If the problem involves geometric concepts, you must know some basic geometry.
To apply mathematics to another field it is not necessary that you be an expert
in that field, but it is very helpful if you know enough so that you can understand
what the expert says when explaining the problem.
The more you know about the field, the more likely it is that you will understand the problem
Some
of the words which frequently come up in applications are:
| area | volume | surface area |
| velocity | acceleration | price |
| percent | percentage | markup |
| marginal rate | discount | current |
| resistance | electric potential | potential energy |
2. Sometimes the problem translates into an equation, sometimes into an inequality, sometimes into a collection of equations and inequalities. This translation process is the most difficult and requires that you know the appropriate mathematics well enough that it comes to mind as a potential method of solving the problem. You must also know the mathematics well enough to apply it correctly.
3. A good and successful strategy in many applications (word problems) is to write two expression for the same quantitiy. This is a good strategy because two expression representing the same quantity must be equal. That observation yields an equation as the mathematical model for the application.
Supplement
to Section 2.3
Supplement
to Section 2.4
The
solution of a first degree inequality in one variable will be one of the four
rays whose graphs are similar to:
The only thing different in different solutions is the number designating the endpoint of the ray.
In the solving process we determine the endpoint, determine whether it is included in the solution set, and determine which direction the solution set extends from the endpoint.
Supplement
to Section 2.5
The
solution of a first degree compound inequality formed by the word AND
in one variable will be the empty set or one of the four intervals whose graphs
are similar to the ones shown here:
The empty set is denoted by the symbol 
The
solution of a first degree compound inequality formed by the word OR
in one variable will be the set of Real Numbers or one of the eight rays whose
graphs are similar to the ones shown here:
Supplement
to Section 2.6
Supplement to Section 2.7