Section 1.1 ­ Linear and Absolute Value Equations
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Equivalent equations and the meaning of solutions
Solving linear equations
Solving absolute value equations
Solving linear equations for one variable
Application problems
Vocabulary:
• equation ­ statement that two expressions are equal
• 3 types: identity, contradiction, conditional
• identity ­ always true for any value that is defined
• contradiction ­ never true
• conditional ­ true for specific value(s)
• solution set ­ set of values that when substituted for the variable will make the equation a true statement
• solution/root ­ any element of the solution set • equivalent equations ­ have same solution set
Examples:
Linear Equations:
• form is ax + b = 0 (a and b are real numbers; a cannot = 0)
• graph is a straight line
• highest exponent of the variable is 1: first degree equation
Examples:
Absolute Value Equations:
Recall definition of absolute value...
Procedures:
Examples:
Section 1.2 Formulas and Applications
Solving formulas for a specific variable:
• Get all of the same variable together on the same side
• Factor out the common variable if necessary
• Isolate the specified variable
Examples:
Distance Problems:
Formula: d = rt (distance = rate x time)
Example: The distance from Shreveport, LA to Austin, TX by one route is 325 miles. If Kevin made the trip in five and a half hours, what was his average speed?
Interest Problems:
Formula: I = Prt (Interest = Principal x rate x time)
Example: Julie invested $1500 in a risky high-tech stock on
January 1st. On July 1st, her stock is worth $2100. She knows
that her investment is very volatile and that it does not earn
interest at a constant rate, but she wants to determine her
average annual rate of return at this point in the year. What
effective annual rate of return has she earned so far?
Geometric Problem: (Note that geometric formulas can be found in
Section 1.2 of your textbook.)
A triangle has a perimeter of 161 miles. The length of each of the
two smaller sides of the triangle is two-thirds the length of the
longest side. Find the length of each side of the triangle.