Chapter 8.8, Problem 30E

To determine

To solve:

The given inequality.

Answer to Problem 30E

The solution for our given inequality would be $t\le -4$ and in interval notation $(-\infty ,-4]$ .

Explanation of Solution

Given:

An inequality:

  $-3t\ge 12$ .

Concept used:

To solve an inequality, we use opposite operations as we use to solve an equation. When we divide or multiply both sides of an inequality by any negative number, it reverses the inequality.

Calculation:

We will solve our given inequality using opposite operations as shown below:

  $\begin{array}{l}-3t\ge 12\text{(Given inequality)}\\ \frac{-3t}{-3}\le \frac{12}{-3}(\text{Dividing by }-3\text{ and flipping the inequality)}\\ t\le -4\end{array}$

Therefore, the solution for our given inequality would be all values of tless than or equal to $-4$ . The solution of our given inequality in interval notation would be $(-\infty ,-4]$ .

Since $-4$ is a solution of our given inequality, so we will have a solid dot at $t=-4$ . Upon graphing solution of our given inequality, we will get: