# 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

# 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