By Kaufman
Grasp algebraic basics with Kaufmann/Schwitters common AND INTERMEDIATE ALGEBRA 5e. examine from transparent and concise motives, a number of examples and diverse challenge units in an easy-to-read structure. The text's 'learn, use & follow' formulation is helping you examine a ability, use the ability to resolve equations, then use it on clear up software difficulties. With this easy, undemanding technique, you'll seize and follow key problem-solving abilities helpful for fulfillment in destiny arithmetic classes.
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Extra info for Elementary and Intermediate Algebra: A Combined Approach
Sample text
5 ϩ (Ϫ3) 2. 7 ϩ (Ϫ4) 7. 8 ϩ (Ϫ2) 8. 12 ϩ (Ϫ7) 3. Ϫ6 ϩ 2 4. Ϫ9 ϩ 4 9. 5 ϩ (Ϫ11) 10. 3 Integers: Addition and Subtraction For Problems 11–30, find each sum. 11. 17 ϩ (Ϫ9) 12. 16 ϩ (Ϫ5) 13. 8 ϩ (Ϫ19) 14. 9 ϩ (Ϫ14) 15. Ϫ7 ϩ (Ϫ8) 16. Ϫ6 ϩ (Ϫ9) 17. Ϫ15 ϩ 8 18. Ϫ22 ϩ 14 19. Ϫ13 ϩ (Ϫ18) 20. Ϫ15 ϩ (Ϫ19) 21. Ϫ27 ϩ 8 22. Ϫ29 ϩ 12 23. 32 ϩ (Ϫ23) 24. 27 ϩ (Ϫ14) 25. Ϫ25 ϩ (Ϫ36) The horizontal format is used extensively in algebra, but occasionally the vertical format shows up. You should therefore have some exposure to the vertical format.
The numerical coefficient of the term Ϫ4abc is 36 Chapter 1 Some Basic Concepts of Arithmetic and Algebra Ϫ4. Because z ϭ 1(z), the numerical coefficient of the term z is 1. Terms that have the same literal factors are called like terms or similar terms. Some examples of similar terms are 3x and 9x 14abc and 29abc 7xy and Ϫ15xy 4z, 9z , and Ϫ14z We can simplify algebraic expressions that contain similar terms by using a form of the distributive property. Consider these examples: 3x ϩ 5x ϭ (3 ϩ 5)x ϭ 8x Ϫ9xy ϩ 7xy ϭ (Ϫ9 ϩ 7)xy ϭ Ϫ2xy 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.
The sum of two negative integers is a negative integer (Ϫ67) ϩ (Ϫ93) ϭ Ϫ(0 Ϫ67 0 ϩ 0 Ϫ93 0 ) ϭ Ϫ(67 ϩ 93) ϭ Ϫ160 20 Chapter 1 Some Basic Concepts of Arithmetic and Algebra One Positive and One Negative Integer The sum of a positive and a negative integer can be found by subtracting the smaller absolute value from the larger absolute value and then giving the result the sign of the original number that has the larger absolute value. If the integers have the same absolute value, then their sum is zero.