Linear Equations and Word Problems for General Studies
Learn about linear equations, inequalities and solving different algebraic word problems in this free online course.Publisher: ADU
CertificationView course modules
This course is the fourth in a series of algebra topics in mathematics. It discusses linear equations in a more advanced way. The free online course begins by introducing you to linear equations and Inequalities in two or more variables. A system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all equations in the system at the same time. Some linear systems may not have a solution and others may have an infinite number of solutions. In order for a linear system to have a unique solution, there must be at least as many equations as there are variables. Even so, this does not guarantee a unique solution. By the end of this course, you should be able to solve systems of equations by graphing, substitution, and addition. You will also be able to identify inconsistent systems of equations containing two variables and express the solution of a system of dependent equations.
Graphing linear inequality can be a bit confusing without the proper knowledge. A linear inequality is the same as a linear equation, only that the inequality sign substitutes the equals sign. The same steps and concepts used to graph linear equations are also applied to graph linear inequalities. The only difference between the two equations is that a linear equation gives a line graph. In contrast, a linear inequality shows the area of the coordinate plane that satisfies the inequality. You will learn about the different steps when graphing a linear inequality and solving systems of linear inequalities graphically. As there are many forms of equations, inequalities also exist in different forms, and quadratic inequality is one of them. A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. A solution to a quadratic inequality is a real number that will produce a true statement when substituted for the variable. You will learn how to solve quadratic inequalities and use number line analysis to find the solution set.
Lastly, the course introduces you to mathematical word problems. A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation. The most common types of word problems in elementary algebra are distance problems, age problems, work problems, percentage problems, mixtures problems, and numbers problems. Word problems commonly include mathematical modeling questions, where data and information about a certain system are given and a student is required to develop a model. For example, Jane had $5.00, then spent $2.00. How much does she have now? These examples are intended to lead students to develop mathematical models on their own and to promote mathematical interest and understanding by analyzing real-life situations. Word problems are a common way to train and test understanding of underlying concepts using a descriptive problem, instead of solely exercising algebraic manipulation or other mechanical skills. By the end of this course, you will be able to analyze and solve different word problems. So, register for this course and start your learning today.Start Course Now
Linear Equations and Inequalities
Linear Equations and Inequalities - Learning Outcomes
The Cartesian Coordinate System
Equations of Lines
Systems of Equations
Linear Equations and Inequalities - Lesson Summary
Linear Equations and Inequalities - Assessment
Word Problems- Learning Outcomes
Age, Coin and Distance Word Problems
Interest and Investment Word Problems
Pythagorean Theorem Word Problems
Word Problems - Lesson Summary
Word Problems - Assessment
Upon the successful completion of this course, you should be able to:
- Solve quadratic inequalities and number line analysis.
- Discuss how to solve the system of equations.
- Describe how to determine if a point lies on a given line.
- Identify the variety of approaches that can be used to find the linear equation.
- Solve a Pythagorean Theorem problem using a single variable and then using two variables.
- Explain how to solve word problems using algebra.
- Identify how to calculate the interest from an investment.
- Solve rectangular frame problems using a single variable and then using several variables.
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