Chapter 5, Problem 22MCQ

To determine

To solve the inequality:

  $-p+4<-9$

And check the solution.

Answer to Problem 22MCQ

  $\left(13,\infty \right)$

Explanation of Solution

Given:

  $-p+4<-9$

Concept Used:

• To check the answer solution for the given inequality
1. First check the solution at end point by converting it into an equation.
2. If the solution is $x<m$, then pick any value of x less than m and check whether it satisfies the inequality.
3. If the solution is $x>m$, then pick any value of x greater than m and check whether it satisfies the inequality.
• Properties of inequality:

1. $b<c\Rightarrow ab<ac,\text{ if }a>0$
2. $b<c\Rightarrow ab>ac,\text{ if }a<0$

Calculation:

To solve the inequality:

  $-p+4<-9$

Subtract both sides of the inequality by $4$ as,

  $\begin{array}{l}-p+4<-9\\ \Rightarrow -p+4-4<-9-4\\ \Rightarrow -p<-13\\ \Rightarrow p>13\end{array}$

Thus, the inequality is true for p strictly greater than $13$ , thus the solution of given inequality in interval form is:

  $\left(13,\infty \right)$

Now, to check the answer solution for the given inequality first check the solution at end point by converting it into an equation. Putting p equals to $13$ in the left hand side as

  $\begin{array}{c}-13+4=-9\\ =\text{Right Hand}\end{array}$

Now put any value any value of p greater than $13$ , say $20$ and check whether it satisfies the inequality, as

  $\begin{array}{l}-20+4=-16\\ \text{And }-16<-9\end{array}$

Since, both conditions are satisfied thus solution of inequality is correct.