College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.5 - Solving Inequalities - 1.5 Assess Your Understanding: 19

Answer

(a) $6 \lt 8$ (b) $-2 \lt 0$ (c) $9 \lt 15$ (d) $-6 \gt -10$

Work Step by Step

RECALL: (1) When a real number is added or subtracted to each side of an inequality, the sense/direction of the inequality is not affected. (2) When a negative number is multiplied to each side of an inequality, the sense/direction of the inequality will change. Use the rules above to obtain: (a) Adding 3 to each side of the given inequality: $\begin{array}{ccc} &3 +3 &\lt &5+3 \\&6 &\lt &8 \end{array}$ (b) Subtracting 5 from each side of the given inequality: $\begin{array}{ccc} &3 -5 &\lt &5-5 \\&-2 &\lt &0 \end{array}$ (c) Multiplying 3 to each side of the given inequality: $\begin{array}{ccc} &3(3) &\lt &3(5) \\&9 &\lt &15 \end{array}$ (d) Multiplying $-2$ to each side of the given inequality: $\begin{array}{ccc} &-2(3) &\gt &-2(5) \\&-6 &\gt &-10 \end{array}$
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