The Collegiate Algebra; Adapted to Colleges and Universities

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1887 edition. Excerpt: ...--So, a b. 353. In the transformation of inequations, it is necessary t J observe when the sign of inequality will be reversed. When this sign is reversed, the tendency of the inequation s said to be changed. Thus, ao and cd, are inequations of the same tendency, and and ab and c d are of opposite tendency. 354. The tendency of an inequation is not changed, 1. By any like operation upon both members, except changing their signs. 2. By adding or multiplying by the corresponding members of an inequation of the same tendency: Provided that in multiplying, the signs of the members be not changed. 3. By subtracting or dividing by the corresponding members of an inequation of opposite tendency: Provided that in dividing, the signs of the members be not changed. 355. The tendency of an inequation is changed, By changing the signs of both members. (Art. 104.) For, 2 3, but--2--3. 356. The tendency of an inequation becomes doubtful, 1. By subtracting or dividing by the corresponding members of an inequation of the same tendency. 2. By adding or multiplying by the corresponding members of an inequation of opposite tendency. For it is evident that if a b and c d, Thus, (1.) 5 15 and 3 6. Subtracting, 2 9. Dividing, . f. (2.) 5 15 and 2 12. Subtracting, 3 = 3. (3.) 5 15 and i3. Dividing, 5 = 5 (4.) 5 6 and 1 4. Dividing, 5 f. Subtracting, 4 2. 357. The Reduction of an Inequation consists in so transforming it that the unknown quantity may stand alone as one member, while the other member contains only known quantities, the value of which is a limit to the value of the unknown quantity in one direction. If two inequations containing the same unknown quantity can be reduced with opposite tendencies, limits in both directions will be found. EXAMPLES. i. Given--...show more

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• Paperback | 60 pages
• 189 x 246 x 3mm | 127g
• Miami Fl, United States
• English
• black & white illustrations
• 123663408X
• 9781236634085