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No Warm up: Practice Problems OnlyTest Friday on Equations

Important Notes for this Weekv6math.blogspot.com --Videos & Power Points

Class Work

This Week:Khan Academy: Please switch topics for Oct. 13, and Oct. 20 October 20 topics due this week, October 13, next week.

Equations Test This Friday: Today, Solve individually or in pairs. Thursday, Review as class.

Terror Drill Awareness: Clarify Instructions

Students without internet access: Your only option now is the library until a router is delivered. Even then, you'll need a laptop, as we cannot put any desktops in the room. (Security)

Please go to Practice Problems Section of Notebook:

Equations Week!!All Equations, All the time

One-Ste

p Two-Step Fractions

,Decim

als

No Solution

All Solutions

|Absolute

Value|

An

d

More

!!!!

Translating, Solving, Writing

Solving Equations is the foundation of Algebra. You cannot do Algebra if you can't solve equations. But you can do Algebra if you can do equations!! Understanding what we do today and tomorrow will determine your entire year. It will make or break you. But they're really not hard, if you pay attention, do the practice problems, believe in yourself and just get it done. Let's do it.

How to Solve More Complex Equations

A. - 8x + 14 = 2(3x - 7) + 10

1. Distribute if available; both sides if necessary 6x - 14

2. Combine like terms on same side of equation if possible = 6x - 14 + 10 = 6x - 4

3. Combine like terms across equation using Inverse Property - 8x - 6x = - 4 - 14; - 14x = -18

4. Eliminate the coefficient thru division. Solve - 14x/-14 = -18/-14; x = 1 2/14; = 1 1/7

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

How to Solve Fractional Equations

There 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:

2. Instead, let's 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

1. Combine like terms if easier. Are there like terms? Yes, there are, but let's not combine them now.

3. Isolate the variable on the left using the inverse property, and divide by the coefficient. x = 28

Your Turn: Write Every Step Needed to Solve

C. 1/2x - 3 = 1/5x + 3 1. Since combining like terms is easy this time, do that first. 1/2x = 1/5x + 6 2. 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 didn't 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

How to Solve Absolute Value Equations

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 equation

2. For the first equation, x = 10

The second equation is: .......

Friday's Test Also Includes

Translating Equations

Decimal Equations

Writing Equations

Everything Else on Today's Review

Class WorkWork independently or in pairs, all problems

You Must Show Each Step for Every Problem to get Credit.

Example: x + 5 = - 7 x = -7 - 5 x = - 12