Bell Ringer Bell Ringer 09/20/1109/20/111.1. Simplify the Simplify the

given fraction: given fraction: 12/14 12/14 NCP.201NCP.201

2.2. Solve for k when Solve for k when 15 + k = 59 15 + k = 59 XEI. 202XEI. 202

3. How many feet is 3. How many feet is 48 inches? 48 inches? BOA. 203BOA. 203

4. 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:Objective:

Solve one step equations by applying Solve one step equations by applying knowledge of inverse operationsknowledge of inverse operations

New SectionNew SectionDateDate Topic(s)Topic(s) Page #Page #

9/__ /119/__ /11 Solving one to two step Solving one to two step equations by applying equations by applying knowledge of the inverse. knowledge of the inverse.

Write what page Write what page are you on?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 (=).

Inverse Operations: opposite operations

+ - • /

- + / •

-Reciprocal: regular or mixed fraction flipped upside down

Evaluating Expressions:Evaluating Expressions:

Given an expression, we can evaluate by Given an expression, we can evaluate by replacing the known value of the variable replacing the known value of the variable in the given expression and solve.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” = -15 + 9 = 6

B. Given x = 7, find the value of -4 + 9x -4 + 9(7) = “-4 plus 9 times 7” = -4 + 63 = 59

Practice Problems:Practice Problems:

Evaluate:Evaluate:

1.1. -3x + 5, when x = -2-3x + 5, when x = -2

2.2. -9 – x, when x = -1-9 – x, when x = -1

3.3. 8x – x, when x = -38x – x, when x = -3

4.4. (1/2)x + 4, when x = 6(1/2)x + 4, when x = 6

5.5. (2 3/5)x – 8, when x = -2(2 3/5)x – 8, when x = -2

How many ways are there How many ways are there to write the same equation?to write the same equation?

There are multiple ways to write an There are multiple ways to write an equation and mean the same thing. equation and mean the same thing.

Example 1:

x + 2 = 5

Can be written:

1x + 2 = 5

2 + x = 5

2 + x = 5

5 = x + 2

5 = 2 + x

Example 2:

2x = 5

Can be written:

(2)x=5 x(2)=5

2•x=5 x•2=5

x2=5 5 = 2x

Example 3:

-2 + x = 5

Can be written:

-2 + 1x = 5

x – 2 = 5

5 = -2 + x

5 = x - 2

What about DIVISION!!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:Practice Problems:Write 2 equal equation to the ones below:Write 2 equal equation to the ones below:

1.1. x + 5= -2 “5 more than x is -2”x + 5= -2 “5 more than x is -2”

2.2. - 4 + x = -6 “ 4 less than x is -6”- 4 + x = -6 “ 4 less than x is -6”

3.3. 3x - 1 = 03x - 1 = 0 “ one less than 3x is 0”“ one less than 3x is 0”

4.4. -5x=3 -5x=3

5.5. x/5 = 8x/5 = 8

6.6. 2x/8 = 12x/8 = 1

Solving Solving ONE STEP EQUATIONS!ONE STEP EQUATIONS!

Use the INVERSE OPERATION! Use the INVERSE OPERATION!

The GOAL: get the variable alone!!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:

107

54 x0

7

5xx – 2.57 = 0 2.5x = - 4

Fractions, Fractions, Fractions,Fractions, Fractions, Fractions,……When an equation involves When an equation involves A FRACTION BEING A FRACTION BEING

MULTIPLIED BY THE VARIABLEMULTIPLIED BY THE VARIABLE, there are a , there are a few tricks you can do to make solving few tricks you can do to make solving SUPER SUPER SIMPLE!SIMPLE!

Trick OPTION 1:

DIVIDE by the fraction using PARENTHASIS!!

Example:

Board Notes

127

4x

Trick OPTION 2:

MULTIPLY by the RECIPROCAL of the fraction!

Example:

Board Notes

127

4x

BE CAREFULL WHICH YOU PICK!

Example:

Board Notes

127

42 x

Partner PracticePartner PracticeSolve the equation for the given variable.Solve the equation for the given variable.1.1. x - 3 = -2 x - 3 = -2 2.2. 7 + x = 17 + x = 13.3. 4 +1x = 124 +1x = 124.4. -4x = 12-4x = 125.5. (-9)x = -27(-9)x = -276.6. 2 = 8x 2 = 8x 7.7. -44x= 121 (write answer as a mixed fraction)-44x= 121 (write answer as a mixed fraction)8.8. DD

9.9. DD

10.10. dd

127

42 x

707

10x

y7

515

HOMEWORK: is Classwork HOMEWORK: is Classwork till the Bell Ringstill the Bell Rings

DateDate Assignment: summarize Assignment: summarize assignment nameassignment name

Due DateDue Date Page #Page # COMPLETION COMPLETION STAMPSTAMP

Solve one step Solve one step equations by applying equations by applying knowledge of inverse knowledge of inverse operationsoperations

What page What page are you are you on?on?

DO NOT FORGET:

-Title, Date, and Name on loose leaf paper

-NEW Page NUMBERED

TOPIC TOPIC NAME & DateNAME & Date

Solve the equation for the given variable.Solve the equation for the given variable.1.1. What is the goal of solving an equation?What is the goal of solving an equation?2.2. x - 5 = -1 x - 5 = -1 3.3. ““7 more than x is 13” set up the equation and solve.7 more than x is 13” set up the equation and solve.4.4. Write an equation that represents, 5 less than x equals 21 and solve.Write an equation that represents, 5 less than x equals 21 and solve.

5.5. 4 +1x = 124 +1x = 126.6. -2x = -12-2x = -127.7. x(9) = -27x(9) = -278.8. 32 = -16x 32 = -16x 9.9. -4x= -11 (write answer as a mixed fraction)-4x= -11 (write answer as a mixed fraction)10.10. What does Reciprocal mean? When do we use the reciprocal?What does Reciprocal mean? When do we use the reciprocal?11.11. There were 31 students in an after school program. They were There were 31 students in an after school program. They were

rewarded for positive behavior and so their coach bought the rewarded for positive behavior and so their coach bought the students pizza. There were 97 slices of pizza. students pizza. There were 97 slices of pizza. Set up an equation Set up an equation that represents this situation. Let x represent the number of slices that represents this situation. Let x represent the number of slices each student would eat.each student would eat.

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