Chapter 2, Problem 7CT

To determine

To solve: the inequality $-7<2c-1<10$ and graph the solution.

Answer to Problem 7CT

  $-3<c<5.5$

Explanation of Solution

Calculation:

Consider the inequality,

  $-7<2c-1<10$

Add 1 to all sides of the inequality,

  $\begin{array}{c}-7+1<2c-1+1<10+1\\ -6<2c<11\end{array}$

Divide all sides of the inequality by 2,

  $\begin{array}{c}\frac{-6}{2}<\frac{2c}{2}<\frac{11}{2}\\ -3<c<5.5\end{array}$

So, the solution of given inequality is $-3<c<5.5$ .

Now, graph $-3<c<5.5$

Now as the inequality contains the symbols $<$ and $>$ , it implies that both $-3$ and $5.5$ are not a solution of $-3<c<5.5$ . So, locate $-3$ and $5.5$ on the number line and use an open circle to represent them.

The solutions of this inequality are all numbers which are greater than -3 but less than 5.5, so shade the number line on the right side of -3 until the open circle at 5.5.

The graph of $-3<c<5.5$ is given below: