Q3. - Algebra 1

Question

Solve each inequality. Then graph it on a number line.

$p-4<-7$

Step-by-Step Solution

Answer

The required value of x is $\left(-\infty ,-3\right)$. The graph on the number line is,

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:

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

Step 2. Solve the inequality for x .

In order to solve the inequality:

$p-4<-7$ 

Add 4 both sides of the inequality, as

 $$\begin{gathered} p-4<-7 \\ p-4+4<-7+4 \\ p<-3 \end{gathered}$$

Thus, the solution of the given inequality is every number is strictly less than $-3$, this can be represented in the interval form, as width="69" style="max-width: none; vertical-align: -4px;" $\left(-\infty ,-3\right)$.

Step 3. Plot the graph on the number line .

Now, in order to sketch the graph of the solution of the inequality, since the interval of solution at left end point $-3$ is strict, so use a hollow circle at point $-3$. And the solution interval at left endpoint $-\infty$, thus every point strictly less than $-3$ is in the solution interval of given inequality. The graph of the solution of inequality is shown below: