Download Lecture Notes 15 - Pioneer Student

Lecture 15 Notes: Section 8.3 & 8.4 – Richard Goldman
MAT116 Algebra I
Basic Mathematics for College Students – 3e
Review
Equation
A statement that two expressions are equal
Variable
An unknown represented by a letter
Addition Property If a = b then a + c = b + c
of Equality
(We can add c to each side without changing the equality of the equation.)
Subtraction
If a = b then a – c = b – c
Property of
(We can subtract c from each side without changing the equality of the equation.)
Equality
Division Property If a = b then a/c = b/c
of Equality
(We can divide each side by c without changing the equality of the equation.)
Multiplication
If a = b then a * c = b * c
Property of
(We can multiply each side by c without changing the equality of the equation.)
Equality
Solving the
Isolate the variable to one side (left) of the equation.
Equation
Strategy
1. Analyze the Problem (Estimate the answer.)
2. Form an Equation
3. Solve the Equation
4. State the Conclusion
5. Check the Results (Does it match your estimate?)
Checking
Substitute the variable with a value and perform the math
solutions
If the values are equal the equation is TRUE – if not it is FALSE
8.3
Algebraic Expressions and Formulas
Algebraic
Mathematical operation that contains both a number and a variable.
Expression
Example: 3 + 2a
Evaluating and
Replace the variable with a number and simplify.
Algebraic
If a = 5 then
Expression
3 + 2a = 3 + 2(5)
3 + 10
13
Formula
Mathematical expression (normally an equation) that state the relationship between two
or more variables. (normally real life relationships)
Speed (Rate) = Distance / Time
8.4
Simplifying Algebraic Expressions and the Distributive Property
Simplifying
Associative Property of Multiplication (grouping)
Expressions
Commutative Property of Multiplication (order)
involving
6(5x) = (6) (5) (x) = 30x
Multiplication
Distributive
Remember: Using the Rules for the Order of Operations:
Property
Example:
2(5 + 3)
2(8)
16
Distributive Property: Applies to expressions of sums or differences
Example:
2(5 + 3)
(2)(5) + (2)(3)
10 + 6
16
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Distributive Property is useful when the expression contains a variable.
Example:
3(x + 7)
3x + 21
Example:
3(x + 3y + 7z + 4)
3x +9y + 21z + 12
Example
-(x + 7)
-x – 7
Distributive Property
a(b + c) = ab + ac or a(b – c) = ab - ac
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