64 Chapter 1 The Set of Real Numbers Solution: a. or The quotient of x and 5 b. The difference of p and the square root of q c. Seven less than n d. Seven less n e. Eight more than the absolute value of w p 1q n 7 7 n 0w0 8 f. x subtracted from 18 Writing an English Phrase as an Algebraic Expression Example 7 Translate each English phrase into an algebraic expression. Then evaluate the expression for a. The product of a and the square root of b b. Twice the sum of b and c c. The difference of twice a and b Solution: a. The product of a and the square root of b Use parentheses to substitute a number for a variable. Substitute and Simplify the radical first. Multiply. a1b 1 211 2 1621142 a 6 b 4. 6 2 12 b. Twice the sum of b and c To compute “twice the sum of b and c,” it is necessary to take the sum first and then multiply by 2.To ensure the proper order, the sum of b and c must be enclosed in parentheses.The proper translation is . Use parentheses to substitute a number for a variable. Substitute and Simplify within the parentheses first. Multiply. 211 2 1 22 21142 12022 b 4 c 20. 21242 48 c. The difference of twice a and b Use parentheses to substitute a number for a variable. Substitute and Multiply first. 2a b 21 2 1 2 2162 142 a 6 b 4. 12 4 8 Subtract. 21b c2 21b c2 a 6, b 4, and c 20. 18 x x 5 x 5 Instructor Note: Show students that 7 less than x would not be written 7 < x. This expression would be worded as 7 is less than x. Classroom Examples: p. 68, Exercises 96 and 102 Answers 21. 22. 23. z 2x ; 4 1 2 1x y2; 6 1y x ; 1 Avoiding Mistakes Recall that “a less than b” is translated as b a. Therefore, the statement “seven less than n” must be translated as n 7, not 7 n. Skill Practice Translate each English phrase to an algebraic expression. Then evaluate the expression for x 3, y 9, z 10. 21. The quotient of the square root of y and x 22. One-half the sum of x and y 23. The difference of z and twice x
miller_introductory_algebra_3e_ch1_3
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