1. Algebraic expressions

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1. Expressions, equations, identities, inequalities

(x+3)² - expression
(x+3)² = 2x + 6 - equation
(x+3)² = x²+6x+9 - identity
(x+3)² > 2x+6 - inequality

Ad. 1
Algebaric expressions consist of numbers, letters representing numbers and other mathematical signs (operation signs, grouping symbols).



Ad. 2
An equation - an equality of 2 algebraic expressions containing at least one variable (unknown)

Variable - any letter used to represent and unspecified number

An equation that can be written in the form ax = b is called:

"an equation of first degree in one variable"

a) solution of an equation - a number that satisfies an equation
b) solution set - the set of solutions

2 equations that have the same solution set are called "equivalent equations"

Ad. 3
Inequalities - inequality of 2 algebraic expressions

a) Solution of an inequality - is a range of values of the variable involved

b) A number line - a straight line with a fixed point called "the origin", unit and direction.