Equations Unit: Vocab: Equation: An equation is a statement that two numbers or expressions are equal. Equations are useful for relating variables and numbers. Expression: An expression is a mathematical term or a sum or difference of mathematical terms that may use numbers, variables, or both. Variable: A variable is a symbol that represents a number. Usually we use letters such as n, t, or x for variables. Inverse Operation: operations that undo something

Number Sentences and Equations Number Sentence: = 10 You already have all the numbers in this number sentence. Single – Step Equation: 7 + B = 10 You don't know one of the values in this number sentence. A variable has been used to take the place of an unknown value. Your job is to solve to find the value of the variable!!! So, instead of a blank or a ? {4 x ____ = 8 or 4 x ? = 8} they put a letter or a variable. m + 12 = 20 You have to use the inverse operation to solve for the variable Inverse operations are operations that undo each other. m = 8Addition and subtraction are inverse operations. Multiplication and division are inverse operations.

Examples: 13 x R = 3914 = 2 + b R - 14 = = 32 + Y

Solve these single – step equations: 1. g ÷ 52 = = j ÷ = 16b c = q + $8.30 = $ z = n + 14 = 83

Single – Step Equations with…NEGATIVES!!! **Solve normally, just pay attention to the signs!!!** Remember your rules! -6 + y = /x = 9

Two – Step Equations First locate the variable and remember…YOU ARE SOLVING FOR THE VARIABLE!!! Take the inverse of whatever is attached on to the variable expression to BOTH sides. Take the inverse of whatever is attached to the variable on BOTH sides. Remember: whatever you do to one side of the equation, you must do to the other side!

Example 40x – 60 = x – = x = x/40 = 160/40 X = 4 Must show all the steps!!!

Two – Step Equations with Distributive Property -4(x-7) =

Practice

Changing Words into an Equation Going from a word expression to an algebraic expression: –Convert the words to variables, numbers, and operation symbols 1)Define the variable 2)Ask yourself are there any key words 3)Write an algebraic expression 4)Simplify

Examples 4 inches more than 10 times your height 10h + 4 James weighs 8 pounds less than 3 times the weight of Kayley 3 k – 8 Five friends pay $8 per hour to rent canoes plus $4 for snacks. Write an expression for the total cost of rental and snacks. Then evaluate the expression for 3 hours. 5 (8h + 4)

Practice