## College Algebra 7th Edition

Published by Brooks Cole

# Chapter 1, Equations and Graphs - Section 1.7 - Solving Inequalities - 1.7 Exercises: 35

#### Answer

$(-\infty, -3.5] \cup [0, +\infty)$ Refer to the image below for the graph.

#### Work Step by Step

First step is to find the zeros of each factor. To find value of $x$ that will make each factor equal to zero, equate each factor to zero then solve each equation: $\begin{array}{ccc} &x=0 &\text{ or } &2x+7=0 \\&x=0 &\text{ or } &2x=-7 \\&x=0 &\text{ or } &x=-\frac{7}{2} \\&x=0 &\text{ or } &x=-3.5 \end{array}$ Next step is to find the intervals. The zeros $-3.5$ and $0$ divide the number line into three intervals, namely: $(-\infty, -3.5), (-3.5, 0), \text{ and } (0, +\infty)$. $\bf\text{Make a table of signs}.$ (refer to the attached image below) $\bf\text{Solve}$ From the table of signs, it can be seen that $x(2x+7)\ge 0$ in the intervals $(-\infty, -3.5)$ and $(0, +\infty)$. The inequality involves $ge$ therefore the endpoints $-3.5$ and $0$ are part of the solution set. Thus, the solution set is $(-\infty, -3.5] \cup [0, +\infty)$. To graph this, plot solid dots at $-3.5$ and $0$ then shade the region to the left of $-3.5$ and the region to the right of $0$. (refer to the attached image in the answer part above)

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