Bell Ringer 09/20/11 1.Simplify the given fraction: 12/14 NCP Solve for k when 15 + k = 59 XEI How many feet is 48 inches? BOA Find the perimeter of the given rectangle. MEA. 201A 5. If 60% of Mr. Birch’s 20 students are passing, how many students are passing? BOA. 202A

Objective:  Solve one step equations by applying knowledge of inverse operations

New Section DateTopic(s) Page # 9/__ /11 Solving one to two step equations by applying knowledge of the inverse. Write what page are you on? VOCABULARY: Mathematical Operations: +, -,, / Expression: Numbers, symbols and operations grouped together that show the value of something Evaluate: find the value of a given expression when the variable is known Equations: mathematical sentence built from expressions using one or more equal signs (=).expressions Inverse Operations: opposite operations +  -  / -  +/  -Reciprocal: regular or mixed fraction flipped upside downfraction

Evaluating Expressions: Given an expression, we can evaluate by replacing the known value of the variable in the given expression and solve. Examples: A. Evaluate 3x + 9 when x= -5. Replace the x with (-5) and always use parentheses.  3 (-5) + 9 = “3 times -5 plus 9” = = 6 B. Given x = 7, find the value of x  (7) = “-4 plus 9 times 7” = = 59

Practice Problems:  Evaluate: 1.-3x + 5, when x = – x, when x = x – x, when x = -3 4.(1/2)x + 4, when x = 6 5.(2 3/5)x – 8, when x = -2

How many ways are there to write the same equation?  There are multiple ways to write an equation and mean the same thing. Example 1: x + 2 = 5 Can be written: 1x + 2 = x = 5 5 = x = 2 + x Example 2: 2x = 5 Can be written: (2)x=5 x(2)=5 2x=5 x2=5 x2=55 = 2x Example 3: -2 + x = 5 Can be written: x = 5 x – 2 = 5 5 = -2 + x 5 = x - 2

What about DIVISION!! Example 4: x/2 = 5 Can be written: Board Rules of division: -Dividing by zero is impossible -zero divided by anything is zero

Practice Problems: Write 2 equal equation to the ones below: 1.x + 5= -2 “5 more than x is -2” x = -6 “ 4 less than x is -6” 3.3x - 1 = 0“ one less than 3x is 0” 4.-5x=3 5.x/5 = 8 6.2x/8 = 1

Solving ONE STEP EQUATIONS! Use the INVERSE OPERATION! The GOAL: get the variable alone!! EXAMPLE 1: x – 2 = - 4 EXAMPLE 2: -3 + x = - 4 EXAMPLE 3: -3x = -6 EXAMPLE 4: 4x = -6 EXAMPLE 5:EXAMPLE 6:EXAMPLE 7:EXAMPLE 8: x – 2.57 = 02.5x = - 4

Fractions, Fractions, Fractions,… When an equation involves A FRACTION BEING MULTIPLIED BY THE VARIABLE, there are a few tricks you can do to make solving SUPER SIMPLE! Trick OPTION 1: DIVIDE by the fraction using PARENTHASIS!! Example: Board Notes Trick OPTION 2: MULTIPLY by the RECIPROCAL of the fraction! Example: Board Notes BE CAREFULL WHICH YOU PICK! Example: Board Notes

Partner Practice Solve the equation for the given variable. 1.x - 3 = x = x = x = 12 5.(-9)x = = 8x 7.-44x= 121 (write answer as a mixed fraction) 8.D 9.D 10.d

HOMEWORK: is Classwork till the Bell Rings Date Assignment: summarize assignment name Due Date Page # COMPLETION STAMP Solve one step equations by applying knowledge of inverse operations What page are you on? DO NOT FORGET: -Title, Date, and Name on loose leaf paper -NEW Page NUMBERED

TOPIC NAME & Date Solve the equation for the given variable. 1.What is the goal of solving an equation? 2.x - 5 = -1 3.“7 more than x is 13” set up the equation and solve. 4.Write an equation that represents, 5 less than x equals 21 and solve x = x = x(9) = = -16x 9.-4x= -11 (write answer as a mixed fraction) 10.What does Reciprocal mean? When do we use the reciprocal? 11.There were 31 students in an after school program. They were rewarded for positive behavior and so their coach bought the students pizza. There were 97 slices of pizza. Set up an equation that represents this situation. Let x represent the number of slices each student would eat. PAGE #