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: 23

Answer

(a) $2x+4 \lt 5$ (b) $2x-4 \lt -3$ (c) $6x+3 \lt 6$ (d) $-4x-2 \gt -4$

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: $\begin{array}{ccc} &2x+1 +3 &\lt &2+3 \\&2x+4 &\lt &5 \end{array}$ (b) Subtracting 5 from each side of the given inequality: $\begin{array}{ccc} &2x+1-5&\lt &2-5 \\&2x-4 &\lt &-3 \end{array}$ (c) Multiplying 3 to each side of the given inequality: $\begin{array}{ccc} &3(2x+1) &\lt &3(2) \\&6x+3 &\lt &6 \\ \end{array}$ (d) Multiplying $-2$ to each side of the given inequality: $\begin{array}{ccc} &-2(2x+1) &\gt &-2(2) \\&-4x-2 &\gt &-4 \end{array}$
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