1. Introduction to Variables, Algebraic Expressions, and Equations
Section 1.8
Introduction to Variables, Algebraic Expressions, and Equations

2. Variables
A symbol ( usually a x ) that represents a quantity in a mathematical expression.

3. Algebraic Expressions
An expression (no equal sign) built up from numbers, variables, and operations.
13x + 22
X is the variable
13 is the coefficient
22 is the constant

4. Example
Define the three parts of the algebraic expression.
5 + 2x

5. Evaluate
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

6. Example
Evaluate the expression 5 + 2x for x = 7

7. Example
Evaluate the expression 3x for x = 5

8. Example
Evaluate the expression 2y2 – 3x2 + 15
for y = 3 and x = 2

9. Equation
 A statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true.
13x + 22 = 35

10. Example
Determine if x = 5 is the solution to the equation 3x – 10 = 5

11. Example
Determine if n = 0 is the solution to the equation 5 (n + 9) = 40

12. Translate Phrased Addition Subtraction Multiplication Division Sum
Difference
Product
Quotient
Plus
Minus
Times
Divide
Added to
Subtract
Multiply
Shared equally among
More than
Less than
Multiply by
Per
Increased by
Less Of
Divided by
Total
Decreased by
Double / Triple
Divided into

13. Example
Write as an algebraic expression. Use x to represent the unknown number.
Twice a number
8 increased by a number
10 minus a number
10 subtracted from a number
The quotient of 6 and a number

14. Example
Translate.
Twenty decreased by twice a number.

15. Example
Translate.
The quotient of twenty and a number, decreased by three.