Algebra Adapted to the Course of Instruction Usually Pursued in the Colleges a
Algebra Adapted to the Course of Instruction Usually Pursued in the Colleges a
Paul a Paul Allen Towne
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2a; B, D _ 91 = 15. Ans. X = So. 5 7 ^ 35 22. - -f 6a = 38. Ans. X=6. 23. - + f=c. 3 a b Solution. - -| — = c (1) = given equation. a b bx-\- ax = abc (2) = (1) X ab. (a -f b) x = abc (3) (Vide ?5, ex. 3. ) x = 7 (4) = required equation. a -f- 6 If a = 2, 6 = 3 and c = 10, then (ex. 14) as = 12. If a = 3, 6 = 4 and c = 14, then x = 24. If a = 5, 5 = 6 and c = 11, then cc = 30. If a = 7, 6 = 4 and c = 22, then x = 56. mx nx abc 24. Solve the equation — -I — — = c. Ans. X = ■ . a b om -\- an If m... = 3, n = 2, a = 4, b = 5 and c = 23, then (ex. 16) x = 20. 82 EQUATIONS OF THE FIE ST DEGEEE. 99. To solve the equation ax -\- d= c — bx. By axiom (3) we may subtract d from both sides of the given equation ; thus : ax -\- d — d = c — bx — d. (2) In the first member -f- d now cancels — d, giving the equation ax — c — bx — d. (3) By axiom (2) we may now add bx to both sides of equation (3) ; thus : ax -}- bx = c — bx -f bx — d. (4) In the second member — bx cancels -f- bx, giving the equation ax -f- bx = c — d.
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