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## New PDF release: College Algebra - With Student Solutions Manual

Posted On April 20, 2018 at 3:24 pm by / Comments Off on New PDF release: College Algebra - With Student Solutions Manual

By Sheldon Jay Axler

ISBN-10: 0470470763

ISBN-13: 9780470470763

ISBN-10: 0470470771

ISBN-13: 9780470470770

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Extra info for College Algebra - With Student Solutions Manual

Sample text

Hence there are no solutions to the equation above with x < 3. The only remaining possibility is that 3 ≤ x ≤ 4. In this case, we have x − 3 ≥ 0 and x − 4 ≤ 0, which implies that |x − 3| = x − 3 and |x − 4| = 4 − x, which implies that x ≥ −3. Thus the set of numbers x such that |x + 3| = x + 3 is the interval [−3, ∞). 17. |x| = x + 1 solution If x ≥ 0, then |x| = x and the equation above becomes the equation x = x + 1, which has no solutions. If x < 0, then |x| = −x and the equation above becomes the equation −x = x + 1, which has the solution x = − 12 .

Because the product of two positive numbers is positive, this implies that (b − a)c is positive. In other words, bc − ac is positive, which means that ac < bc, as desired. Now consider the case where c < 0. We are still assuming that a < b, which means that b − a is positive. Because the product of a positive number and a negative number is negative, this implies that (b − a)c is negative. In other words, bc − ac is negative, which means that ac > bc, as desired. An important special case of the result above is obtained by setting c = −1, which gives the following result: For example, from the inequality 2 < 3 we can conclude that −2 > −3.

Positive and negative numbers • A number is called positive if it is right of 0 on the real line. • A number is called negative if it is left of 0 on the real line. Every number is either right of 0, left of 0, or equal to 0. Thus every number is either positive, negative, or 0. 3 5 2 2 115 76 1 2 1 3 3 negative numbers 0 1 2 3 3 1 12 7 2 257 101 3 positive numbers All of the following properties should already be familiar to you. Example: 2+3=5 (−2) + (−3) = −5 Algebraic properties of positive and negative numbers • The sum of two positive numbers is positive.