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Additional resources for Schaum's Outline of Elementary Algebra (3rd Edition) (Schaum's Outlines Series)
The selling price of $90,000 should be the cost minus the loss. Hence, $90,000 $150,000 Ϫ $60,000 $90,000 ϭ $90,000 2 ᎏᎏ 5 The cost was $150,000. 1. 2. Ans. 3. 2) Translate into an equation, letting n represent the number. ) a) b) c) d) e) What number diminished by 8 equals 13? Two-thirds of what number equals 10? Three times the sum of a number and 6 is 33. What is the number? What number increased by 20 equals 3 times the same number? What number increased by 5 equals twice the same number decreased by 4?
X ϭ 50 Check: x ᎏᎏ Ϫ 3 ϭ 7 5 50 ᎏᎏ Ϫ 3 7 5 10 Ϫ 3 7 7ϭ7 SOLVING EQUATIONS WITH LIKE TERMS ON THE SAME SIDE Solve each equation. ) a) 8n ϩ 4n Ϫ 3 ϭ 9 b) 13n ϩ 4 ϩ n ϭ 39 12n Ϫ 3 ϭ 9 14n ϩ 4 ϭ 39 A3 12n ϩ 3 ϭ 13 12n12 n ϭ 12 S4 112nϪ4 ϭ Ϫ4 14n 1x2nϭ 35 c) S7 n 10 ϭ 7 ϩ n Ϫ ᎏᎏ 2 n 10 ϭ 7 ϩ ᎏᎏ 2 Ϫ7 ϭ Ϫ712n n 3ϭ ᎏᎏ 2 34 SIMPLE EQUATIONS AND THEIR SOLUTIONS D2 12n 12 ᎏᎏ ϭ ᎏᎏ 12 12 D4 Ans. nϭ1 Ans. 14n 35 ᎏᎏ ϭ ᎏᎏ 14 14 [CHAP. 2 n M2 2 и 3 ϭ ᎏᎏ 2 2 n ϭ 2ᎏ12ᎏ Ans. 3. SOLVING EQUATIONS WITH LIKE TERMS ON BOTH SIDES Solve each equation.
Thus, 2n ϩ 3n ϭ 5n and x ϩ y ϭ y ϩ x are identities since there is no restriction on the values that n, x, and y may have. A solution to an equation is any number which when substituted for the unknown, will make both sides of the equation equal. A solution is said to satisfy the equation. Thus, 6 is a solution of 2n ϭ 12, while 5 or any other number is not. Checking an equation is the process of substituting a particular value for an unknown to see if the value will make both sides equal. Thus, check in 2x ϩ 3 ϭ 11 for x ϭ 4 and x ϭ 5 as follows: 2x ϩ 3 ϭ 11 2(4) ϩ 3 11 8 ϩ 3 11 11 ϭ 11 2x ϩ 3 ϭ 11 2(5) ϩ 3 11 10 ϩ 3 11 13 ≠ 11 NOTE.