Equations and Expressions

# Objective

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

Methods of manipulation include simplifying, substituting, and solving.

# Key Terminology

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Caption text  Term | Definition | Part of Speech

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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

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# Equations

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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):

2 a + 3 a − 30 = 10 2 a + 3 a + 30 = + 30 2 a + 3 a = 40 5 a = 40 5 a 5 = 40 5 a = 8 {\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

## See Also

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* Equations
* Expressions