By Revathi Narasimhan
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Extra info for College algebra and trigonometry : building concepts and connections
Algebraic Expressions In algebra, letters such as x and y are known as variables. You can use a variable to represent an unknown quantity. For example, if you earn x dollars per hour and your friend earns $2 more than you per hour, then x ϩ 2 represents the amount in dollars per hour earned by your friend. When you combine variables and numbers using multiplication, division, addition, and subtraction, as well as powers and roots, you get an algebraic expression. We are often interested in finding the value of an algebraic expression for a given value of a variable.
T Ϫ 5)2 11. (z ϩ 6) ϩ (5z ϩ 8) 47. (s ϩ 6)2 48. (Ϫv ϩ 3)2 12. (2x Ϫ 3) Ϫ (x ϩ 6) 49. (5t ϩ 4)2 50. (7x ϩ 1)2 13. (Ϫ5y 2 ϩ 6y) Ϫ ( y Ϫ 3) 51. (6v Ϫ 3)2 52. (4x ϩ 5)2 14. (Ϫ9x 2 Ϫ 32x ϩ 14) ϩ (Ϫ2x 2 ϩ 15x Ϫ 6) 53. (3z Ϫ 1)2 54. (2y ϩ 1)2 15. (Ϫ9x 3 ϩ 6x 2 Ϫ 20x ϩ 3) ϩ (x 2 Ϫ 5x Ϫ 6) 55. (6 Ϫ 5t)2 56. (Ϫ9 ϩ 2u)2 16. (5t 3 ϩ 16t Ϫ 12) Ϫ (2t 3 Ϫ 4t 2 ϩ t) ϩ (Ϫ5t 2 Ϫ 3t ϩ 7) 57. (v ϩ 9)(v Ϫ 9) 58. (z Ϫ 7)(z ϩ 7) 17. (3x 4 Ϫ x 3 ϩ x 4 Ϫ 4) ϩ (x 5 ϩ 7x 3 Ϫ 3x 2 ϩ 5) 59. (9s ϩ 7)(7 Ϫ 9s) 60. (Ϫ6 ϩ 5t)(Ϫ5t Ϫ 6) 18.
The interval (Ϫϱ, 4͔ consists of all real numbers less than or equal to 4. ✔ Check It Out 2: Graph the interval ͓3, 5͔ on the number line, and give a verbal description of the interval. 1 lists different types of inequalities, their corresponding interval notations, and their graphs on the number line. 4 in interval notation. ᭤Solution The interval consists of all numbers greater than or equal to Ϫ3 and less than 2. The number 2 is not included, since it is represented by an open circle. Thus, in interval notation, the set of points is written as ͓Ϫ3, 2).
College algebra and trigonometry : building concepts and connections by Revathi Narasimhan