Chapter 3.3, Problem 2STP

For Exercises $1-5,$ choose the correct letter.

What is the solution of $-3\ge -\frac{2}{3}z?$

F. $z\le -\frac{9}{2}$

G. $z\le \frac{9}{2}$

H. $z\ge -\frac{9}{2}$

I. $z\ge \frac{9}{2}$

To determine

To solve the inequality $-3\ge -\frac{2}{3}z$ .

Answer to Problem 2STP

Solution is $z\ge \frac{9}{2}$ and option I is correct.

Explanation of Solution

Given:

  $-3\ge -\frac{2}{3}z$

Concept used:

When multiplying or dividing each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed to produce an equivalent inequality.

Calculation:

  $-3\ge -\frac{2}{3}z$

Multiplying 3 on both sides, we get

  $\begin{array}{l}-3\times 3\ge -\frac{2}{3}z\times 3\\ \Rightarrow -9\ge -2z\end{array}$

Dividing by $-2$ on both sides, we get

  $\begin{array}{l}\frac{-9}{-2}\le \frac{-2z}{-2}\\ \Rightarrow \frac{9}{2}\le z\\ \Rightarrow z\ge \frac{9}{2}\end{array}$

Hence option I is correct.