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Lin Equ per 1.notebook
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December 10, 2015
Oct 209:19 PM
Module 4Linear Equations
Dec 110:40 PM
Lesson 1Writing Equations Using Symbols
Lin Equ per 1.notebook
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December 10, 2015
Feb 2310:31 PM
Reviewing Distributive Property5(b 6)
10(5 + x)
3(9 + a) = 54
Nov 2711:15 AM
Mathematical Statement vs. Equation
The number 1,157 is the sum of the squares of two consecutive odd integers divided by the difference between the two consecutive odd integers.
1,157 = x2 + (x + x2)(x + 2) x
Expression vs. Equation
Lin Equ per 1.notebook
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December 10, 2015
Nov 2711:30 AM
How would you write the following mathematical statements as an expression or equation?
a) The square of half the number.
b) A whole number has the property that when the square of half the number is subtracted from five times the number, we get back the number itself.
c) When a number is subtracted from itself, the difference is zero.
Nov 2711:30 AM
How would you write the following mathematical statements as an expression or equation?
d) Paulo has a certain amount of money. If he spends six dollars, then he has 1/4 of the original amount left..
e) When a fraction of 57 is taken away from 57, what remains exceeds 2/3 of 57 by 4.
f) The sum of three consecutive integers is 372.
g) The sum of three consecutive odd integers is 93.
Lin Equ per 1.notebook
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December 10, 2015
Nov 2711:38 AM
Take out all the pages for Lesson 1 and complete Exercise 15 with a partner.
1. Analyze the Written Statement by highlighting/underlining important facts
2. Use numbers and a variable to represent the important facts
Nov 303:33 PM
Lin Equ per 1.notebook
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December 10, 2015
Nov 127:33 PM
Assignment: ENY 4.1 PS #19
Complete the Exit Ticket
Nov 51:07 PM
Lesson 2Linear and Nonlinear Expressions
Lin Equ per 1.notebook
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December 10, 2015
Dec 212:39 PM
1. Analyze the Written Statement by highlighting/underlining important facts
2. Use numbers and a variable to represent the important facts
Dec 23:55 PM
Put the following expressions in two groups:
Lin Equ per 1.notebook
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December 10, 2015
Dec 24:05 PM
What are the requirements of a linear expression?
(3x 17) 2x2 + 9x + 5
vocabularyterm constant variable coefficient reciprocal
non linearlinear
Dec 24:07 PM
Write each of the following written statements as an expression. We will determine whether it is linear or nonlinear. If it is nonlinear, explain why. 1. The sum of a number and four times the number.
2. The square of the difference between a number and 10.
3. Twice a number subtracted from four times a number, added to 15.
4. The sum of twice a number and four times a number subtracted from the number squared.
Take out all the pages for Lesson 2.
Lin Equ per 1.notebook
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December 10, 2015
Dec 24:28 PM
Complete #9‐12 by writing each of the following written statements as an expression. Then determine whether it is linear or nonlinear. If it is nonlinear, explain why.
9. x x x
10. 45 + x
11. 10 + 2x
12. 2(4x + 5)
12
23 linear expression
linear expression
linear expression
nonlinear expression
Nov 127:33 PM
Assignment: ENY 4.2 PS #112
Complete the Exit Ticket
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December 10, 2015
Nov 64:38 PM
Lesson 3Linear Equations in x
Nov 2711:47 AM
Applying the Commutative and/or Associative Properties and
Combining like terms
7x + 9 + 6 + 3x
5 + 9x 7 + 2x9 .
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December 10, 2015
Dec 410:55 AM
What are the Order of Operations?
Dec 48:08 PM
Look at the following equations and determine which are true and explain how you know they are true.
1) 4 + 1 = 5 3) 21 6 = 152) 6 + 5 = 16 4) 6 2 = 1
Lin Equ per 1.notebook
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December 10, 2015
Dec 410:55 AM
Linear Equations in x is a statement about equality to find all the numbers x that make the equation true.
Is 4 + 15x = 49?What would be a value that would make this equation true?
Is this the only value that would make the equation true?
What would be a value that would make this equation false?
Dec 48:19 PM
1) Linear Equation in x: 4 + 15x = 49
If x = 3 does it make the equation true?
Does x = 2 satisfy the equation: 4 + 15x = 49?
2) Is 5 a solution to the equation: 8x 19 = 4 7x
Is 1 a solution to the equation?
Lin Equ per 1.notebook
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December 10, 2015
Dec 48:26 PM
Linear Equation in x: 3(x + 9) = 4x 15 + 7xFirst we need to transform the expressions into fewer terms or
standard form. How can we do that?
3(x + 9) = 4x 15 + 7x
Is 3 a solution to the equation?
Is a solution to the equation?12
Dec 48:37 PM
Does x = 6 satisfy the equation: 2x + 11 5x = 5 6x
What do we need to do the expressions before we substitute x for 6?
2x + 11 5x = 5 6x
Lin Equ per 1.notebook
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December 10, 2015
Dec 48:40 PM
Take out all the pages for Lesson 3.
Remember to combine like terms or convert the equation to standard form first.
Nov 127:33 PM
Assignment: ENY 4.3 PS #14
Complete the Exit Ticket
Lin Equ per 1.notebook
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December 10, 2015
Nov 410:28 PM
Solving Linear Equations
Dec 89:08 PM
How would you solve the equation: 4x + 1 = 13?
Share with the class:
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December 10, 2015
Dec 89:08 PM
How would you solve the equation: 3x + 2 x = 11x + 9
Is it as easy to solve this equation as the first one? Why?
Dec 89:41 PM
Properties of EqualityIf you add, subtract, multiply, or divide a rational number to both expressions, is the equation still equal and true?
Steps to Solving EquationsGet the variable on one side of the equal sign and a value on the other side
1. combine like terms through addition and/or subtraction2. isolate the variable through multiplication and/or division
Lin Equ per 1.notebook
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December 10, 2015
Dec 89:44 PM
7x 24 x = 12
Always go back and check your solution to make sure the equation is TRUE!
Dec 89:47 PM
Always go back and check your solution to make sure the equation is TRUE!
7x + 9 = 3x + 9x +12
Lin Equ per 1.notebook
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December 10, 2015
Dec 89:47 PM
3x 2 x = 10x + 14
Always go back and check your solution to make sure the equation is TRUE!
Dec 89:47 PM
3(2x 5) = 3(x + 11)
Always go back and check your solution to make sure the equation is TRUE!
Lin Equ per 1.notebook
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December 10, 2015
Nov 2712:54 PM
5(3 − x) − 2(4 − 3x) = 11 − 2(x − 1) 6 − 4(x + 3) = 2(x − 1)
5(1 − 2x) + 2(3 − x) = 3(x + 4) + 14 6x + 2 = 29 − 3x
Always go back and check your solution to make sure the equation is TRUE!
Have students work these in groups.
Nov 127:33 PM
Complete the Exit Ticket below:
2(3x + 2) = 2x 1 + x7x 4 + x = 12
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December 10, 2015
Nov 127:33 PM
Assignment: copied page: SHOW YOUR WORK FOR EACH STEP IN YOUR WORK BOOK
Complete the Exit Ticket below:
7x 4 + x = 12
2(3x + 2) = 2x 1 + x
Nov 2712:39 PM
Solving More Linear Equations
Lin Equ per 1.notebook
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December 10, 2015
Dec 68:34 PM
15x + 20 2x = 7x + 6x 33
Dec 68:25 PM
20 3x + 9 2 = 11x 1
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December 10, 2015
Dec 68:35 PM
17 10x + 45 = 6x 10 + 4
Nov 127:33 PM
Assignment: copied page: Choose 5 problems from each side. Choose to do complete proofs to check your solution.
Complete the Exit Ticket below:
12 + 5x 8 = 12x 10
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December 10, 2015
Dec 97:58 AM
Steps to Solving Equations
Dec 97:59 AM
Do I have to ________________?
Do I have ________________?
Do I have ________________ on both sides?
Do I have ________________ on both sides?
Is the variable ________________ ?
2 + 5(x + 3) 3(x 4) = x + 2(2x + 4)
Lin Equ per 1.notebook
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December 10, 2015
Nov 2712:39 PM
Solving Linear Equations with
Rational Numbers
Dec 89:41 PM
Properties of EqualityIf you add, subtract, multiply, or divide a rational number to both expressions, is the equation still equal and true?
Steps to Solving EquationsGet the variable on one side of the equal sign and a value on the other side
1. combine like terms through addition and/or subtraction2. isolate the variable through multiplication and/or division
Lin Equ per 1.notebook
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December 10, 2015
Dec 89:44 PM
x + 18 = x14
Always go back and check your solution to make sure the equation is TRUE!
Dec 89:44 PM
Always go back and check your solution to make sure the equation is TRUE!
Lin Equ per 1.notebook
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December 10, 2015
Dec 89:44 PM
Always go back and check your solution to make sure the equation is TRUE!
Nov 127:33 PM
Lin Equ per 1.notebook
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December 10, 2015
Nov 127:33 PM
Assignment: copied page: SHOW YOUR WORK FOR EACH STEP IN YOUR WORK BOOK
Complete the Exit Ticket below:
Nov 119:03 PM
Lesson 6Solutions of Linear Equations
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December 10, 2015
Dec 89:08 PM
Think about it:What is the "best" first step to begin solving this linear equation and why?
4x + 3(4x + 7) = 4( 7x + 3) 3
Share with your table:
Share with the class:
Try solving this equation at your table. Show your work on the big white board. Write it neatly because you will be sharing it with the class.
Explain how you solved the linear equation.
Dec 1110:13 AM
4x + 3(4x + 7) = 4( 7x + 3) 3
4x + 12x + 21 = 28x + 12 3
16x = 28x + 928x = 28x
8x = 98 = 8 x = 9 8
or ‐1 18
Lin Equ per 1.notebook
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December 10, 2015
Dec 810:11 PM
20 (3x 9) 2 = (11x + 1)What is the "best" first step to begin solving this linear equation and why?
Dec 97:14 PM
5(3x + 4) 2x = 7x 3(2x + 11)
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December 10, 2015
Dec 810:11 PM
(4x + 6) 2 = (5x + 9)12
Check for TRUE!
17 5(2x 9) = (6x + 10) + 4
5(3 − x) − 2(4 − 3x) = 11 − 2(x − 1)
Nov 127:33 PM
Assignment: S.19 choose 5 problems
Complete the Exit Ticket.
