By Deborah Hughes-Hallett, William G. McCallum, Eric Connally
Shape is said to operate. An plane wing has the shape it does as a result of its lifting functionality. The pillars of the Parthenon and the girders of a skyscraper are formed to the aim of aiding their huge constructions. equally, the shape of an algebraic expression or equation displays its functionality. Algebra: shape and serve as initial version introduces every one function--linear, strength, quadratic, exponential, polynomial--and provides a research of the fundamental type of expressions for that functionality. Readers are inspired to ascertain the fundamental types, see how they're developed, and think about the position of every part. in the course of the textual content, there are instruments sections put on the ends of chapters to assist readers collect the talents they should practice easy algebraic manipulations.
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Extra resources for Algebra: Form and Function
T + 1 = t 19. t(1 + t(1 + t(1 + t))) = 1 24. x + 3 = 8 25. 2x = 10 26. x − 4 = 15 27. 28. 12 = x − 7 29. 24 = 6w 20. Which of the numbers in (a)–(d) is a solution to the equation? −3x2 + 3x + 8 = 3x(x + 1) + 1 2 (a) 1 (b) 0 (c) −1 (d) 2 30. T = 10 3 x 3 =1 31. 20 − x = 13 32. 5x = 20 33. t + 5 = 20 34. w/5 = 20 35. y − 5 = 20 36. 20 = 5 − x PROBLEMS 37. The value of a computer t years after it is purchased is: Value of the computer = 3500 − 700t. (a) What is value of the computer when it is purchased?
94. Group expressions (a)–(f) together so that expressions in each group are equivalent. Note that some groups may contain only one expression. 2 3 5 10 (a) + (b) (c) k k 2k 2k 74. Write an expression for the average amount spent per ticket. 75. Suppose v = 2w and q = 4p. Rewrite the expression in Problem 73 in terms of w and q. In Problems 76–82, both a and x are positive. What is the effect of increasing a on the value of the expression? Does the value increase? Decrease? Remain unchanged? 76.
But how can we be sure of finding a solution to an equation, and how can we be sure that we have found all the solutions? For a more complicated equation, we try to find a simpler equation having the same solutions. A common way of doing this is to perform the same operation on both sides of the equation. Example 1 What operation transforms the first equation into the second equation? Check to see that the solutions of the second equation are also solutions of the first equation. 6 = 40 a2 = 64 (a) We add 10 to both sides of the equation to get 2x − 10 + 10 = 12 + 10 2x = 22.