Chapter 1: Section 4 Notes
By the end of the section, you should be able to:
- Solve algebraic equations
- Create equations to model situations.
Definitions:
- Equation: a statement that two expressions are equal (=).
- Solution of an Equation: a value, or values of the variable that make the equation true.
- Inverse Operations: operations that “undo” each other (addition and subtraction, multiplication and division, etc.).
- Identity: an equation that is true for EVERY possible value of the variable.
- Literal Equation: an equation that uses at least two different letters as variables. With literal equations, the solution of the equation is “in terms of” the other variable(s).
Properties of Equality
Solving Algebraic Equations
Things/Steps to Remember:
- The goal is to find the solution of the equation by isolating (getting by itself) a variable on one side using inverse operations.
Equations that have NO solutions and Identity Equations
Things/Steps to Remember:
- If the equation simplifies to a statement that is never true such as: , the equation has no solution.:
- If the equation simplifies to an a statement that is always true such as: , the equation has infinite solutions. This is an identity.
- If the equation simplifies to a statement that is sometimes true such as: , then the only solution is the value that makes it true (which is true only when x has the value of 3).
Solving Literal Equations
Things/Steps to Remember:
- When solving in terms of a variable, that is the variable that is not isolated (by itself).
Equations that Model Situations
Things/Steps to Remember:
- Drawing a picture or diagram is helpful when creating an algebraic equation or model.
A2 Section 1.4 Worksheet
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