CLO 2: Determine the solution sets of all types of algebraic equations

TOPIC 2: EQUATIONS

OVERVIEW

This module will be discussing the concepts governing equations and inequalities. We are going to learn on how to solve equations, how to establish equations, and how to construct equations that reflects real-world phenomena and problems. We shall learn the importance of equation and inequalities in modelling as it is part of engineering skills.

LEARNING OUTCOME

At the end of this module, you should be able to:

1. Solve linear equations.

2. Solve one variable in terms of others.

3. Solve quadratic equations.

Subtopic: SOLUTIONS OF A CONDITIONAL EQUATION

These are values of the unknowns which make both members equal. The solutions are said to satisfy the equation. If only one unknown is involved the solutions are also called roots. In example 1, the value for x as 2 will serve as a solution to the equation x + 6 = 8. (Larson, 2011)

EXAMPLE:

Solve the equation: 7x − 4 = 3x + 8

Solution:

7x − 4 = 3x + 8 Given Equation

(7x − 4) + 4 = (3x + 8) + 4 Add 4

7x = 3x + 12 Simplify

7x − 3x = (3x + 12) − 3x Subtract 3

4x = 12 Simplify

1/4 (4x) =1/4 (12) Multiply by 1/4

x = 3 Simplify

Note: You must substitute the root to the original equation in order to check if the root is indeed the solution of the equation.

REFERENCES:

Larson, R. (2011). Algebra and Trigonometry, 8th Edition. Belmont, CA: Cengage Learning.

Spiegel, M. (1998). Schaum's Outline: College Algebra , 2nd Edition. USA: McGraw-Hill.

Watson, J. (2012). Algebra and Trigonometry. Belmont, CA: Cengage Learning.

PROBLEM SET 2

Reflection on Learning

For the second problem set, this particular problem for me was somewhat easy because I had background knowledge of some of the basic formulas. What makes it hard is the fact that there are real-life problems that use a combination of formulas and don't lie on a specific formula alone. The problem above integrates different formulas for the solution to be possible and that's the difficult part in solving that kind of problem. Now to answer that problem, it is important first to know about the process of answering the problem to get the desired point. But to be specific, the problem requires the combination of formulas regarding square and rectangle that brought a huge impact on answering the equation. What I learned here is to be more appropriate in using my tools in problem solving because we'll never know if it would be beneficial for us in the long run.