Chapter 2, Problem 8CT

To determine

To solve: the inequality $-2\le 4-3a\le 13$ and graph the solution.

Answer to Problem 8CT

  $-3\le a\le 2$

Explanation of Solution

Calculation:

Consider the inequality,

  $-2\le 4-3a\le 13$

Subtract 4 from all sides of the inequality,

  $\begin{array}{c}-2-4\le 4-3a-4\le 13-4\\ -6\le -3a\le 9\end{array}$

Divide all sides of the inequality by -3 (since the inequality is being divided by a negative number so the signs of the inequality will be reversed),

  $\begin{array}{c}\frac{-6}{-3}\ge \frac{-3a}{-3}\ge \frac{9}{-3}\\ 2\ge a\ge -3\end{array}$

So, the solution of given inequality is $-3\le a\le 2$ .

Now, graph $-3\le a\le 2$

Now as the inequality contains the symbols $\le$ and $\ge$ , it implies that both $-3$ and $2$ are solutions of $-3\le a\le 2$ . So, locate $-3$ and $2$ on the number line and use closed circles to represent them.

The inequality includes all numbers which are greater than or equal to -3 but less than or equal to 2, so shade the number line on the right side of -3 until the closed circle at 2.

The graph of $-3\le a\le 2$ is given below: