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# Final equations week1

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### Final equations week1

1. 1. Today Welcome Back No Warm up: Practice Problems Only Test Friday on Equations Important Notes for this Weekv6math.blogspot.com --Videos & Power Points Class Work
2. 2. This Week:Khan Academy: Please switch topics for Oct. 13, and Oct. 20October 20 topics due this week, October 13, next week.Equations Test This Friday: Today, Solve individually or inpairs. Thursday, Review as class.Terror Drill Awareness: Clarify InstructionsStudents without internet access: Your only option now isthe library until a router is delivered. Even then, youll need alaptop, as we cannot put any desktops in the room. (Security)Please go to Practice Problems Section of Notebook:
3. 3. Equations Week!! All Equations, All the time And More!!!!Translating, Solving, Writing
4. 4. Solving Equations is the foundation ofAlgebra. You cannot do Algebra if youcant solve equations. But you can doAlgebra if you can do equations!! Understanding what we do today andtomorrow will determine your entire year.It will make or break you. But theyrereally not hard, if you pay attention, do thepractice problems, believe in yourself andjust get it done. Lets do it.
5. 5. How to Solve More Complex EquationsA. - 8x + 14 = 2(3x - 7) + 101. Distribute if available; both sides if necessary 6x - 142. Combine like terms on same side of equation if possible = 6x - 14 + 10 = 6x - 43. Combine like terms across equation using Inverse Property - 8x - 6x = - 4 - 14; - 14x = -184. Eliminate the coefficient thru division. Solve - 14x/-14 = -18/-14; x = 1 2/14; = 1 1/7
6. 6. Your Turn: Write Every Step Needed to Solve B. 10 - 5(2x + 10) = 5 (x + 2) 1. 10 - 10x -50 = 5x + 10 2. - 10x - 40 = 5x + 10 3. - 10x - 5x = 10 - 40; -15x = - 30 4. - 15x/-15 = - 30/-15; x = - 2
7. 7. How to Solve Fractional EquationsThere are several ways fractions can appear in equations, but the goal is always to clear the fractions the easiest way possible. C. 1/3x - 1/3 = 9 The steps: 1. Combine like terms if easier. Are there like terms? Yes, there are, but lets not combine them now. 2. Instead, lets clear the fractions by multiplying each term by the number which cancels the denominator (3/1) (⅓x) - (3/1) (⅓) = 9(3/1); x - 1 = 27 3. Isolate the variable on the left using the inverse property, and divide by the coefficient. x = 28
8. 8. Your Turn: Write Every Step Needed to SolveC. 1/2x - 3 = 1/5x + 31. Since combining like terms is easy this time, do that first. 1/2x = 1/5x + 62. Here we have 2 different denominators, so we find the Least Common Denominator (LCD); The LCD of 2 and 5 is 10. Now we have: 5/10x = 2/10x + 6.Why didnt we multiply the 6 by 10 also? Because we did not change the size of the fractions at all! ½ and 5/10 is the same number. What is our next step? Multiply all three terms by 10/1; Our equation now looks like: 5x = 2x + 60; Completing the steps we get: 5x - 2x = 3x = 60; x = 20 Finally, checking our work: 10 - 3 = 4 + 3; 7 = 7
9. 9. How to Solve Absolute Value Equations
10. 10. Your Turn: Write Every Step Needed to Solve D. - 13 = - |x + 3|1. In other words, the opposite of 13 = the opposite of |x + 3|The first equation: |x + 3| = 13; solve this and the second equation2. For the first equation, x = 10 The second equation is: .......
11. 11. Fridays Test Also Includes Translating Equations Decimal Equations Writing Equations Everything Else on Todays Review
12. 12. Class Work Work independently or in pairs, all problemsYou Must Show Each Step for Every Problem toget Credit. Example: x + 5 = - 7 x = -7 - 5 x = - 12