Objective- To recognize symbols, variables, and types of sentences used in algebra.
Equalities
Inequalities
=
Equals- is the same as Congruent- same size and shape Similar- same shape
< >
Is less than Is greater than Is less than or equal to Approx. equal to Not equal to
=
What is a variable?
A variable represents an unknown value.
1) 3 + ___ = 10
2) 6 +
= 9
3) 8 + x = 12 4) 5 + = 8
These are all variables
Why use letters to represent variables?
Expressions vs. Equations
Sentences
Expressions Numerical Equations Inequalities
2+3 5(8)
-4
2+3=5 4 + 2(3) = 10 X 4 = 13 11= 3 + 2m
9 6y
-5>3
Variable
X+7
8
- 3y
-
-4<8
Open sentences Open sentences have solutions and can be solved.
Open sentences have solutions and can be solved.
Variable Equations
Variable Inequalities
-
4+m=7 4 4
-
Solutions
5 + y < 91 5 5
-
m=3
y < 86
Identify each as an expression, sentence, open sentence, equation, or inequality.
1) 3x + 5 = 11 Sentence, open sentence, equation
2) 7 < 2(5) + 3 Sentence, inequality 3) 5(3) - 2 Expression 4) 6m + 2 > 3 Sentence, open sentence, inequality
Multiplication and Division Symbols
Ways to Multiply Ways to Divide
5x7
5
8 4 8 4 8/4
7
5(7) 5 7
With variables...
5 x 5x 5axy
4
8
Squares vs. Square Roots
Squares
Square Roots
1 1 2 2 4 2 3 9 2 4 16 2 5 25 2 6 36
2
1 1 4 2 9 3 16 4 25 5 36 6
Solve the following:
x 100
x 100
2
x 10
One Solution
x 10 x 10
Two Solutions
or
Follow the pattern!
10 10
2
x x
2
7 7
2
True if x is positive.
6 6
2
x 3
( 3) 3
2
3 3
2
9 3
Not true if x is negative.
x
2
Follow the pattern!
10 10
2
x x
2
7 7
2
x x
2
6 6
2
( 3) 3
2
3 3
2
9 3
True Always!
x x
2
Solved a different way:
x 100
x 100
2
x 10
One Solution
x 100 x 10
2
x 10 x 10
Two Solutions or