Chapter 3.2, Problem 28PPE

To determine

To find:

Solution of the given inequality. To graph it and to check its solutions.

Answer to Problem 28PPE

Solution of the given inequality in interval form is $p=(3,\infty )$ that is shown in below graph:

  

Explanation of Solution

Given information:

Inequality $p-1\frac{1}{2}>1\frac{1}{2}$ 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:

Add $1\frac{1}{2}$ each side in given inequality,

  $\begin{array}{l}p-1\frac{1}{2}+1\frac{1}{2}>1\frac{1}{2}+1\frac{1}{2}\\ \Rightarrow p>\frac{3}{2}+\frac{3}{2}=\frac{6}{2}\\ \Rightarrow p>3\end{array}$

On number line, show this solution as:

  

Check: Substitute a value from above solution set, say, $p=4,$ in given inequality,

  $\begin{array}{l}4-1\frac{1}{2}=4-\frac{3}{2}=\frac{5}{2}\\ >1\frac{1}{2}\end{array}$

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 3, as sown in above graph also.