Q22. - Algebra 1

Question

Solve each inequality. Check your solution. 

$-p+4<-9$

Step-by-Step Solution

Answer

The required value of p is $\left(13,\infty \right)$.

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\le \text{ or }\ge$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

$$\begin{gathered} 1.b\le c\Rightarrow b\pm a\le c\pm a \\ \begin{array}{l}2.b\le c\Rightarrow ab\le ac,\text{ if }a>0\\ 3.b\le c\Rightarrow ab\ge ac,\text{ if }a<0\end{array} \end{gathered}$$

Step 2. Solve the inequality for x .

In order to solve the inequality:

$-p+4<-9$ 

Subtract both sides of the inequality by 4, as

$$\begin{gathered} -p+4<-9 \\ -p+4-4<-9-4 \\ -p<-13 \\ p>13 \end{gathered}$$ 

Thus, the inequality is true for p strictly greater than 13, thus the solution of given inequality in interval form is, as $\left(13,\infty \right)$.

Step 3. Check the solution .

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

$$\begin{gathered} -13+4=-9 \\ =\text{Right Hand side} \end{gathered}$$

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

$$\begin{gathered} -p+4<-9 \\ -20+4<-9 \\ -16<-9\left[\text{True}\right] \end{gathered}$$

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