Mathematics Bridge Program: Linear Equations
Mathematics Bridge Program ©2002 DeVry University
Algebra
Chapter 4
Solving Linear Equations
1. Definitions Linear Equation Solution Property of Equality
2. Solving Linear Equations Distributive Property Eliminating Fractions
3. Solving for One Variable in a Formula
4. Summary: Process for Solving Linear Equations
5. Worked out Solutions for Exercises
4.1 Definitions:
Linear Equations:
An equation is a statement that two expressions have the same value:
[pic]
Any number or the value of the variable that makes an equation a true statement is called a solution of the equation. The process of finding the solution of an equation is called solving the equation for the variable or unknown. You can also call it finding x (or y, or whatever variable you are using). All solutions should be checked by substituting back into the original equation, and seeing if that will give a true statement. If you solved [pic] to give you [pic], you will easily see if you have the right answer by substituting [pic] back into [pic] (you don’t).
Linear equation in one variable (with one unknown):
A linear equation in one variable can be written in the form
[pic], where a, b, and c are real numbers and a[pic]0.
Note that the variable (x) is raised to the first power: that’s how you recognize a linear equation.
Examples of linear equations: [pic] [pic] can be manipulated to be written in the standard form of [pic]
Property of Equality:
If a, b, and c are real numbers, [pic] are equivalent equations
[pic] are equivalent equations
[pic] are equivalent equations, [pic]
This property guarantees that by adding, subtracting (as in adding a negative), multiplying or dividing by the same quantity on both sides you end up with equivalent equations and the solution of the equation is not changed.
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Algebra
Chapter 4
Solving Linear Equations
1. Definitions Linear Equation Solution Property of Equality
2. Solving Linear Equations Distributive Property Eliminating Fractions
3. Solving for One Variable in a Formula
4. Summary: Process for Solving Linear Equations
5. Worked out Solutions for Exercises
4.1 Definitions:
Linear Equations:
An equation is a statement that two expressions have the same value:
[pic]
Any number or the value of the variable that makes an equation a true statement is called a solution of the equation. The process of finding the solution of an equation is called solving the equation for the variable or unknown. You can also call it finding x (or y, or whatever variable you are using). All solutions should be checked by substituting back into the original equation, and seeing if that will give a true statement. If you solved [pic] to give you [pic], you will easily see if you have the right answer by substituting [pic] back into [pic] (you don’t).
Linear equation in one variable (with one unknown):
A linear equation in one variable can be written in the form
[pic], where a, b, and c are real numbers and a[pic]0.
Note that the variable (x) is raised to the first power: that’s how you recognize a linear equation.
Examples of linear equations: [pic] [pic] can be manipulated to be written in the standard form of [pic]
Property of Equality:
If a, b, and c are real numbers, [pic] are equivalent equations
[pic] are equivalent equations
[pic] are equivalent equations, [pic]
This property guarantees that by adding, subtracting (as in adding a negative), multiplying or dividing by the same quantity on both sides you end up with equivalent equations and the solution of the equation is not changed.
Just