Chapter 3.2, Problem 35PPE

To determine

To find:

Solution of the inequality $2<9+c$ . To graph it and to check its solutions.

Answer to Problem 35PPE

Solution of the given inequality in interval form is $c=(-7,\infty )$ that is shown red in below graph:

  

Explanation of Solution

Given information:

Inequality $2<9+c$ is given.

Concept used:

Get the solution of given inequality by removing all terms, associated with unknown variable. Do just opposite operation of that term, each side to eliminate its term.

Calculation:

Subtract 9 each side in given inequality,

  $\begin{array}{l}2-9<9-9+c\\ \Rightarrow -7<c\end{array}$

On number line, show this solution as:

  

Check: Substitute a value from above solution set, say, $c=0$ in given inequality,

  $\begin{array}{l}2<9+0\\ \Rightarrow 2<9\end{array}$

that is true, so given solution set is correct.

Conclusion:

So, solution of the given inequality is the set of all the real values, those are greater than $-7$ , as shown in above graph also.