Chapter 3.3, Problem 25PPE

To determine

To solve: the inequality $18b\le -3$ . Graph and check the solution.

Answer to Problem 25PPE

  $b\le -\frac{1}{6}$

Explanation of Solution

Given:

The inequality: $18b\le -3$

Concept Used:

Let a, b and c be real numbers where $c>0$ . Then,

If $a>b$ , then $\frac{a}{c}>\frac{b}{c}$

Divide both sides of the given inequality by 18,

  $\frac{18b}{18}\le -\frac{3}{18}$

Simplify both sides of the inequality,

  $b\le -\frac{1}{6}$

Now, to graph the inequality $b\le -\frac{1}{6}$ , draw a number line with a closed circle at $-\frac{1}{6}$ . And since b is less than or equal to $-\frac{1}{6}$ , so draw a line going towards left from the closed circle at $-\frac{1}{6}$ . Thus, the required graph is:

  

Now, to check the above solution, pick any number from the red line section of the above number line and substitute in given inequality,

So, let $b=-1$ . Then,

  $\begin{array}{c}18\left(-1\right)\le -3\\ -18\le -3\end{array}$

Which is a true statement.

Conclusion:

Hence, the solution of the given inequality is $b\le -\frac{1}{6}$ .