By Bob Miller

A is for Algebra-and that is the grade you will pull if you use Bob Miller's uncomplicated consultant to the maths direction each college-bound child needs to take With 8 books and greater than 30 years of hard-core school room adventure, Bob Miller is the pissed off student's ally. He breaks down the complexities of each challenge into easy-to-understand items that any math-phobe can understand-and this totally up to date moment version of Bob Miller's Algebra for the Clueless covers every little thing a you must comprehend to excel in Algebra I and II.

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**Extra resources for Algebra for the Clueless **

**Example text**

Click here for terms of use. 36 BOB MILLER’S ALGEBRA FOR THE CLUELESS EXAMPLE 2— Given 5x − 2 = 2x − 23, 5 is not a root, while −7 is a root. N OT E If there are two letters t in a problem, you mus know what letter to solve for. 5(5) − 2 2(5) − 23 5(−7) − 2 2(−7) − 23 23 ≠ −13 5 is not a root −37 = −37 −7 is a root EXAMPLE 3— 6x − 2a = 4x − 10a has a root x = −4a. 6(−4a) − 2a 4(−4a) − 10a −26a = −26a Soooo, x = −4a is a root. There are 3 basic types of equations we will deal with. 1. Contradiction—An equation with no solution or a false equation.

Contradiction—An equation with no solution or a false equation. EXAMPLE 4— 9+7=4 You cannot add one to a number and get the same number. x=x+1 We will do only a few of these. 2. Identity—An equation that is true for all values it is defined for. EXAMPLE 5— 2x + 3x = 5x No matter what value we substitute, 2 times a number plus 3 times that number will always be 5 times that number. First-Degree Equations 37 EXAMPLE 6— 5 6 11 ᎏ+ᎏ=ᎏ x x x It is not defined for x = 0 (remember, you can’t divide by 0), but for any other number 5/x + 6/x = 11/x.

And so on. 3 means +3. EXAMPLE 1— Graph the set −4, −1, 0, 3. –5 –4 –3 –2 –1 0 1 2 3 4 23 Copyright © 2006, 1999 by The McGraw-Hill Companies, Inc. Click here for terms of use. 24 BOB MILLER’S ALGEBRA FOR THE CLUELESS EXAMPLE 2— Graph all even integers between −6 and 7. ) –6 –4 –2 0 2 4 6 8 Now that we know what an integer is, we would like to add, subtract, multiply, and divide them. ADDITION For adding, you should think about money: + means gain and − means loss. EXAMPLE 3— 7+5 Think (don’t write) (+7) + (+5) Gain 7; gain 5 more.