By Jerome E. Kaufmann, Karen L. Schwitters
Starting ALGEBRA employs a confirmed, three-step problem-solving approach--learn a ability, use the ability to unravel equations, after which use the equations to unravel software problems--to maintain scholars thinking about development talents and reinforcing them via perform. this easy and simple technique, in an easy-to-read structure, has helped many scholars clutch and follow basic problem-solving abilities. The rigorously established pedagogy comprises studying ambitions, distinct examples to increase ideas, perform routines, an intensive choice of problem-set workouts, and well-organized end-of-chapter studies and exams. also, the fresh and uncluttered layout is helping maintain scholars considering the ideas whereas minimizing distractions. difficulties and examples reference a vast array of subject matters, in addition to occupation parts reminiscent of electronics, mechanics, and health and wellbeing, displaying scholars that arithmetic is a part of way of life. additionally, as steered via the yank Mathematical organization of Two-Year faculties, many uncomplicated geometric thoughts are built-in within the book's problem-solving units. The text's source package--anchored through more desirable WebAssign, an internet homework administration tool--saves teachers time whereas additionally delivering extra aid and skill-building perform for college students outdoors of sophistication.
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Additional info for Beginning Algebra (Available 2010 Titles Enhanced Web Assign)
EXAMPLE 15 Simplify 2 3 ϩ 4 3 # 1 3 Ϫ 5 2 # 1 . 5 Solution 3 2 3 1 1 3 2 1 ϩ # Ϫ # ϭ ϩ Ϫ 4 3 5 2 5 4 5 10 ϭ Perform the multiplications 8 2 15 ϩ 8 Ϫ 2 21 15 ϩ Ϫ ϭ ϭ 20 20 20 20 20 ▼ PRACTICE YOUR SKILL EXAMPLE 16 Simplify 1 4 1 3 3 ϩ # Ϫ # . 14 4 7 2 7 Simplify 3 8 1 1 5 Ϭ ϩ aϪ b a b ϩ . 5 5 2 3 12 Change to equivalent fractions and combine the numerators ■ Solution 3 8 1 1 5 3 5 1 1 5 Ϭ ϩ aϪ b a b ϩ ϭ # ϩ aϪ b a b ϩ 5 5 2 3 12 5 8 2 3 12 ϭ 3 Ϫ1 5 ϩ ϩ 8 6 12 Change division to multiply by the reciprocal 50 Chapter 1 Basic Concepts of Arithmetic and Algebra ϭ ϭ ϭ 9 Ϫ4 10 ϩ ϩ 24 24 24 9 ϩ 1Ϫ42 ϩ 10 Change to equivalent fractions 24 15 5 ϭ 24 8 Reduce!
133 is not divisible by 3, because 1 ϩ 3 ϩ 3 ϭ 7 and 7 is not divisible by 3. Rule for 5 A whole number is divisible by 5 if and only if the units digit of its base-10 numeral is divisible by 5. ) EXAMPLES 115 is divisible by 5, because 5 is divisible by 5. 172 is not divisible by 5, because 2 is not divisible by 5. 36 Chapter 1 Basic Concepts of Arithmetic and Algebra Rule for 9 A whole number is divisible by 9 if and only if the sum of the digits of its base-10 numeral is divisible by 9. EXAMPLES 765 is divisible by 9, because 7 ϩ 6 ϩ 5 ϭ 18 and 18 is divisible by 9.
3 Use of Properties 29 18abc Ϫ 27abc ϭ (18 Ϫ 27)abc ϭ [18 ϩ (Ϫ27)]abc ϭ Ϫ9abc 4x ϩ x ϭ (4 ϩ 1)x Don’t forget that x ϭ 1(x) ϭ 5x More complicated expressions might ﬁrst require that we rearrange terms by using the commutative property. EXAMPLE 7 Simplify these algebraic expressions: (a) 7x ϩ 3y ϩ 9x ϩ 5y (b) 9a Ϫ 4 Ϫ 13a ϩ 6 Solution (a) 7x ϩ 3y ϩ 9x ϩ 5y ϭ 7x ϩ 9x ϩ 3y ϩ 5y ϭ (7 ϩ 9)x ϩ (3 ϩ 5)y Commutative property for addition Distributive property ϭ 16x ϩ 8y (b) 9a Ϫ 4 Ϫ 13a ϩ 6 ϭ 9a ϩ (Ϫ4) ϩ (Ϫ13a) ϩ 6 ϭ 9a ϩ (Ϫ13a) ϩ (Ϫ4) ϩ 6 ϭ [9 ϩ (Ϫ13)]a ϩ 2 Commutative property for addition Distributive property ϭ Ϫ4a ϩ 2 ▼ PRACTICE YOUR SKILL Simplify these algebraic expressions: (a) 6a Ϫ 3a ϩ 7 Ϫ 5a ϩ 1 (b) 2y Ϫ 3x ϩ 5x Ϫ 6y ■ As you become more adept at handling the various simplifying steps, you may want to do the steps mentally and thereby go directly from the given expression to the simpliﬁed form.