Objective

In this lesson, we will cover variables, expressions, equations, and methods of manipulating them.

Methods of manipulation include simplifying, substituting, and solving.

Key Terminology

Caption text

Term	Definition	Part of Speech
Variable	A symbol used to represent a quantity that can change. Variables are numbers.	Noun
Expression	A representation of a quantity that uses numbers or variables, or the mathematical product of both.	Noun
Equation	A statement of equality using the symbol ${\displaystyle =}$. The quantities on each side of the equal sign are the same a each other.	Noun
Solution	A value or values that make equations true.	Noun
Manipulate	Modify an expression or an equation in a way that changes what's written on the page.	Verb
Solve	Look for solutions	Verb
Simplify	Rewrite an expression as a less complicated expression	Verb
Substitute	Replace a value with another thing of equal value	Verb

Variables and Expressions

Equations

A simple equation:

2a+3b+c = 0

This equation has 3 variables (a,b and c);; 3 terms (2a, 3b and c);; and this equation is an equality, because here is an equal sign (=) between both sides of the equation.

Next: solution to a simple algebra problem. Solve the following equation for (a):

${\displaystyle {\begin{aligned}2a+3a-30&=10\\{\phantom {2a+3a}}+30&{\phantom {=}}+30\\2a+3a&=40\\5a&=40\\{\frac {5a}{5}}&={\frac {40}{5}}\\a&=8\end{aligned}}}$

- -- - - - - - - - - Some trig stuff:

sin ɵ = Opposite-Side/Hypotenuse

cos ɵ = Adjacent-Side/Hypotenuse

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