By Deborah Hughes-Hallett, William G. McCallum, Eric Connally
Shape is said to operate. An aircraft 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 assisting their tremendous 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 offers a research of the elemental kind of expressions for that functionality. Readers are inspired to envision the elemental varieties, see how they're developed, and look at the function 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 simple algebraic manipulations.
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Extra resources for Algebra: Form and Function
This statement looks like an equation. In order to distinguish this use of equations, we refer to x + x = 2x as an identity. An identity is really a special equation, one that is satisfied by all values of the variables. For simple identities, we can sometimes see that the two expressions on either side are equivalent by visualizing them on the number line. 1, indicate an interval of length 1 − x, and then use this to indicate an interval of length 1 − (1 − x). What two expressions does this suggest are equivalent?
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? (b) Write an equation whose solution is the time when the computer is worth nothing. 38. 25 each. Write an equation whose solution is the number of ice cream cones he can buy, and find the number. 39. Hannah has $100 in a bank account and deposits $75 more. Write an equation whose solution is the amount she needs to deposit for the balance to be $300, and find the amount.
B) We can combine only the z 3 terms: −z 3 + 5z 3 − 3z = (−1 + 5)z 3 − 3z = 4z 3 − 3z. Example 6 Simplify 3(x + 3) − x − 14. Solution In order to combine like terms we first have to rewrite 3(x + 3) as 3x + 3 · 3 = 3x + 9. Then, reordering and combining like terms, we obtain Combine Combine 3(x + 3) − x − 14 = 3x + 9 − x − 14 = 3x − x + 9 − 14 = 2x − 5. The rule of arithmetic that allows us to rewrite 3(x + 3) as 3x + 9 is called the distributive law, which is the subject of the next section. In fact, combining like terms is really a special case of the distributive law.
Algebra: Form and Function by Deborah Hughes-Hallett, William G. McCallum, Eric Connally