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: 24

Answer

(a) $4-2x \gt 8$ (b) $-2x-4 \gt 0$ (c) $3-6x\gt 15$ (d) $-2+4x \lt -10$

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: $\begin{array}{ccc} &1-2x+3 &\gt &5+3 \\&4-2x &\gt &8 \end{array}$ (b) Subtracting 5 from each side of the given inequality: $\begin{array}{ccc} &1-2x-5&\gt &5-5 \\&-2x-4 &\gt &0 \end{array}$ (c) Multiplying 3 to each side of the given inequality: $\begin{array}{ccc} &3(1-2x) &\gt &3(5) \\&3-6x &\gt &15 \\ \end{array}$ (d) Multiplying $-2$ to each side of the given inequality: $\begin{array}{ccc} &-2(1-2x) &\lt &-2(5) \\&-2-(-4x) &\lt &-10 \\&-2+4x &\lt -10 \end{array}$
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