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

Methods of manipulation include simplifying, substituting, and solving.

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

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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• Equations
• Expressions