By Rhonda Huettenmueller
* Explains the right way to comprehend algebra with no need a mathematical historical past
* makes use of sensible examples and genuine info
* contains a whole part dedicated to notice difficulties and fractions
Read or Download Algebra Demystified: A Self Teaching Guide PDF
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Extra info for Algebra Demystified: A Self Teaching Guide
If you must cancel 2þx the x out of , you must rewrite the fraction: x CHAPTER 2 Introduction to Variables 2þx 2 x 2 ¼ þ ¼ þ 1: x x x x Simply because a plus or minus sign appears in a fraction does not auto3þx matically mean that canceling is not appropriate. For instance ¼1 3 þx because any nonzero quantity divided by itself is one. Examples ð2 þ 3xÞðx À 1Þ 2 þ 3x x À 1 ¼ Á ¼ x À 1: 2 þ 3x 2 þ 3x 1 The reason 2 + 3x can be canceled is that 2 + 3x is a factor of (2 + 3x)(x À 1). 2ðx þ 7Þð3x þ 1Þ 2 ðx þ 7Þð3x þ 1Þ ¼ Á ¼ ðx þ 7Þð3x þ 1Þ 2 2 1 15ðx þ 6Þðx À 2Þ 3 Á 5ðx þ 6Þðx À 2Þ 3ðx À 2Þ 5ðx þ 6Þ ¼ ¼ Á ¼ 5ðx þ 6Þ 3ðx À 2Þ 3ðx À 2Þ 3ðx À 2Þ 1 Practice 1: 3xy ¼ 2x 2: 8x ¼ 4 3: 30xy ¼ 16y 4: 72x ¼ 18xy 5: xðx À 6Þ ¼ 2x 6: 6xyð2x À 1Þ ¼ 3x 39 CHAPTER 2 Introduction to Variables 40 7: ð5x þ 16Þð2x þ 7Þ ¼ 6ð2x þ 7Þ 8: 24xðy þ 8Þðx þ 1Þ ¼ 15xðy þ 8Þ 9: 150xyð2x þ 17Þð8x À 3Þ ¼ 48y Solutions 1: 3xy 3y x 3y ¼ Á ¼ 2x 2 x 2 2: 8x 2x 4 ¼ Á ¼ 2x 4 1 4 3: 30xy 15x 2y 15x ¼ Á ¼ 16y 8 2y 8 4: 72x 4 18x 4 ¼ Á ¼ 18xy y 18x y 5: xðx À 6Þ x À 6 x x À 6 ¼ Á ¼ 2x 2 x 2 6: 6xyð2x À 1Þ 2yð2x À 1Þ 3x ¼ Á ¼ 2yð2x À 1Þ 3x 1 3x 7: ð5x þ 16Þð2x þ 7Þ 5x þ 16 2x þ 7 5x þ 16 ¼ Á ¼ 6ð2x þ 7Þ 6 2x þ 7 6 8: 24xðy þ 8Þðx þ 1Þ 8ðx þ 1Þ 3xðy þ 8Þ 8ðx þ 1Þ ¼ Á ¼ 15xðy þ 8Þ 5 3xðy þ 8Þ 5 9: 150xyð2x þ 17Þð8x À 3Þ 25xð2x þ 17Þð8x À 3Þ 6y ¼ Á 48y 8 6y 25xð2x þ 17Þð8x À 3Þ ¼ 8 CHAPTER 2 Introduction to Variables 41 Operations on Fractions with Variables Multiplication of fractions with variables is done in exactly the same way as multiplication of fractions without variables—multiply the numerators and multiply the denominators.
16. (b) (a) (a) (d) This page intentionally left blank. CHAPTER 2 Introduction to Variables A variable is a symbol for a number whose value is unknown. A variable might represent quantities at diﬀerent times. ’’ The value of your earnings varies depending on the number of hours worked. If an equation has one variable, we can use algebra to determine what value the variable is representing. Variables are treated like numbers because they are numbers. For instance 2 þ x means two plus the quantity x and 2x means two times the quantity x (when no operation sign is given, the operation is assumed to be multiplication).
The expression 3x þ 4 means three times x plus four. This is not the same as 3x þ 4x which is three x’s plus four x’s for a total of seven x’s: 3x þ 4x ¼ 7x. If you are working with variables and want to check whether the expression you have computed is really equal to the expression with which you started, take some larger prime number, not a factor of anything else in the expression, and plug it into both the original expression and the last one. If the resulting numbers are the same, it is very likely that the ﬁrst and last expressions are equal.
Algebra Demystified: A Self Teaching Guide by Rhonda Huettenmueller