Symbols, Variables, and Types of Sentences used in Algebra. Equalities Inequalities < Is less than = Equals- is the same as > Is greater than Congruent- same size and shape Is less than or equal to Approx. equal to Similar- same shape = Not equal to

What is a variable? A variable represents an unknown value. 1) 3 + ___ = 10 2) 6 + = 9 These are all variables 3) 8 + x = 12 4) 5 + = 8

Expressions vs. Equations Sentences Expressions Equations Inequalities 2 + 3 2 + 3 = 5 9 - 5 > 3 5(8) - 4 Numerical 4 + 2(3) = 10 X - 4 = 13 X + 7 6y - 4 < 8 Variable 8 - 3y 11= 3 + 2m Open sentences Open sentences have solutions and can be solved.

- 4 - 4 - 5 - 5 Open sentences have solutions and can be solved. Variable Equations Variable Inequalities 4 + m = 7 5 + y < 91 - 4 - 4 - 5 - 5 m = 3 y < 86 Solutions

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 8 4 5 x 7 8 5 7 4 5(7) 8 / 4 5 7 With variables... 5 x 4 8 5x 5axy

Squares vs. Square Roots

Solve the following: or One Solution Two Solutions

Follow the pattern! True if x is positive. Not true if x is negative.

Follow the pattern! True Always!

Solved a different way: One Solution or Two Solutions