# Chapter 1 - Section 1.5 - Solving Inequalities - 1.5 Assess Your Understanding - Page 127: 21

(a) $7 \gt 0$ (b) $-1 \gt -8$ (c) $12 \gt -9$ (d) $-8 \lt 6$

#### 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: $\begin{array}{ccc} &3 +4 &\gt &3+(-3) \\&7 &\gt &0 \end{array}$ (b) Subtracting 5 from each side of the given inequality: $\begin{array}{ccc} &4 -5 &\gt &-3-5 \\&-1&\gt &-8 \end{array}$ (c) Multiplying 3 to each side of the given inequality: $\begin{array}{ccc} &3(4) &\gt &3(-3) \\&12 &\gt &-9 \end{array}$ (d) Multiplying $-2$ to each side of the given inequality: $\begin{array}{ccc} &-2(4) &\lt &-2(-3) \\&-8 &\lt &6 \end{array}$

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