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

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

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

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

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

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

Example Evaluate the expression 3x2 + 12 for x = 5

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

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

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

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

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

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

Example Translate. Twenty decreased by twice a number.

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