Module 4 Linear Equations Oct 20 9:19 PM Lesson 1 Writing Equations Using Symbols Dec 1 10:40 PM 1
5(b 6) Reviewing Distributive Property 10( 5 + x) 3(9 + a) = 54 Feb 23 10:31 PM 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 + x 2 ) (x + 2) x Expression vs. Equation Nov 27 11:15 AM 2
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 27 11:30 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. Nov 27 11:30 AM 3
1. Analyze the Written Statement by highlighting/underlining important facts 2. Use numbers and a variable to represent the important facts Take out all the pages for Lesson 1 and complete Exercise 1 5 with a partner. Nov 27 11:38 AM Nov 30 3:33 PM 4
Complete the Exit Ticket Assignment: ENY 4.1 PS #1 9 Nov 12 7:33 PM Lesson 2 Linear and Nonlinear Expressions Nov 5 1:07 PM 5
1. Analyze the Written Statement by highlighting/underlining important facts 2. Use numbers and a variable to represent the important facts Dec 2 12:39 PM Put the following expressions in two groups: Dec 2 3:55 PM 6
(3x 17) 2x 2 + 9x + 5 linear non linear What are the requirements of a linear expression? vocabulary term constant variable coefficient reciprocal Dec 2 4:05 PM Take out all the pages for Lesson 2. 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. Dec 2 4:07 PM 7
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. 1 2 9. x x x 2 3 10. 45 + x 11. 10 + 2x 12. 2(4x + 5) nonlinear expression linear expression linear expression linear expression Dec 2 4:28 PM Complete the Exit Ticket Assignment: ENY 4.2 PS #1 12 Nov 12 7:33 PM 8
Lesson 3 Linear Equations in x Nov 6 4:38 PM Applying the Commutative and/or Associative Properties and Combining like terms 7x + 9 + 6 + 3x 5 + 9x. 7 + 2x 9 Nov 27 11:47 AM 9
What are the Order of Operations? Dec 4 10:55 AM 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 = 15 2) 6 + 5 = 16 4) 6 2 = 1 Dec 4 8:08 PM 10
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? Linear Equations in x is a statement about equality to find all the numbers x that make the equation true. Dec 4 10:55 AM 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? Dec 4 8:19 PM 11
Linear Equation in x: 3(x + 9) = 4x 15 + 7x First 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 1 2 a solution to the equation? Dec 4 8:26 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 Dec 4 8:37 PM 12
Remember to combine like terms or convert the equation to standard form first. Take out all the pages for Lesson 3. Dec 4 8:40 PM Complete the Exit Ticket Assignment: ENY 4.3 PS #1 4 Nov 12 7:33 PM 13
Solving Linear Equations Nov 4 10:28 PM How would you solve the equation: 4x + 1 = 13? Share with the class: Dec 8 9:08 PM 14
Is it as easy to solve this equation as the first one? Why? How would you solve the equation: 3x + 2 x = 11x + 9 Dec 8 9:08 PM Properties of Equality If you add, subtract, multiply, or divide a rational number to both expressions, is the equation still equal and true? Steps to Solving Equations Get the variable on one side of the equal sign and a value on the other side 1. combine like terms through addition and/or subtraction 2. isolate the variable through multiplication and/or division Dec 8 9:41 PM 15
7x 24 x = 12 Always go back and check your solution to make sure the equation is TRUE! Dec 8 9:44 PM 7x + 9 = 3x + 9x +12 Always go back and check your solution to make sure the equation is TRUE! Dec 8 9:47 PM 16
3x 2 x = 10x + 14 Always go back and check your solution to make sure the equation is TRUE! Dec 8 9:47 PM 3(2x 5) = 3(x + 11) Always go back and check your solution to make sure the equation is TRUE! Dec 8 9:47 PM 17
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 Have students work these in groups. Always go back and check your solution to make sure the equation is TRUE! Nov 27 12:54 PM Complete the Exit Ticket below: 7x 4 + x = 12 2(3x + 2) = 2x 1 + x Nov 12 7:33 PM 18
Complete the Exit Ticket below: 7x 4 + x = 12 2(3x + 2) = 2x 1 + x Assignment: copied page: SHOW YOUR WORK FOR EACH STEP IN YOUR WORK BOOK Nov 12 7:33 PM Solving More Linear Equations Nov 27 12:39 PM 19
15x + 20 2x = 7x + 6x 33 Dec 6 8:34 PM 20 3x + 9 2 = 11x 1 Dec 6 8:25 PM 20
17 10x + 45 = 6x 10 + 4 Dec 6 8:35 PM Complete the Exit Ticket below: 12 + 5x 8 = 12x 10 Assignment: copied page: Choose 5 problems from each side. Choose to do complete proofs to check your solution. Nov 12 7:33 PM 21
Steps to Solving Equations Dec 9 7:58 AM Do I have to? 2 + 5(x + 3) 3(x 4) = x + 2(2x + 4) Do I have? Do I have on both sides? Do I have on both sides? Is the variable? Dec 9 7:59 AM 22
Solving Linear Equations with Rational Numbers Nov 27 12:39 PM Properties of Equality If you add, subtract, multiply, or divide a rational number to both expressions, is the equation still equal and true? Steps to Solving Equations Get the variable on one side of the equal sign and a value on the other side 1. combine like terms through addition and/or subtraction 2. isolate the variable through multiplication and/or division Dec 8 9:41 PM 23
1 4 x + 18 = x Always go back and check your solution to make sure the equation is TRUE! Dec 8 9:44 PM Always go back and check your solution to make sure the equation is TRUE! Dec 8 9:44 PM 24
Always go back and check your solution to make sure the equation is TRUE! Dec 8 9:44 PM Nov 12 7:33 PM 25
Complete the Exit Ticket below: Assignment: copied page: SHOW YOUR WORK FOR EACH STEP IN YOUR WORK BOOK Nov 12 7:33 PM Lesson 6 Solutions of Linear Equations Nov 11 9:03 PM 26
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: 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. Share with the class: Explain how you solved the linear equation. Dec 8 9:08 PM 4x + 3(4x + 7) = 4( 7x + 3) 3 4x + 12x + 21 = 28x + 12 3 16x = 28x + 9 28x = 28x 8x = 9 8 = 8 x = 9 8 or 1 1 8 Dec 11 10:13 AM 27
20 (3x 9) 2 = ( 11x + 1) What is the "best" first step to begin solving this linear equation and why? Dec 8 10:11 PM 5(3x + 4) 2x = 7x 3( 2x + 11) Dec 9 7:14 PM 28
1 2 (4x + 6) 2 = (5x + 9) 17 5(2x 9) = ( 6x + 10) + 4 5(3 x) 2(4 3x) = 11 2(x 1) Check for TRUE! Dec 8 10:11 PM Complete the Exit Ticket. Assignment: S.19 choose 5 problems Nov 12 7:33 PM 29