Question

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

$\mathit{x}\mathbf{-}\mathbf{9}\mathbf{<}\mathbf{-}\mathbf{4}$

Short answer

The solution of the given inequality$x-9<-4$ is $\mathit{x}\mathbf{<}\mathbf{5}$.

The graph of the solution of the given inequality $x-9<-4$that is graph of $x<5$is:

Step-by-step solution

Step 1. Write the addition property of inequalities.

The addition property of inequalities states that if the same number is added to each side of a true inequality, the resulting inequality is also true that is:

1. If $a>b$, then $a+c>b+c$.
2. If $a<b$, then $a+c<b+c$.

Step 2. Solve the given inequality x−9<−4.

The solution of the given inequality $x-9<-4$is:

$\begin{array}{c}x-9<-4\\ x-9+9<-4+9\left(\text{byusingadditionpropertyofinequality}\right)\\ x<5\end{array}$

Therefore, the solution of the given inequality$x-9<-4$ is $x<5$.

Step 3. Draw the graph of the inequality x<5.

The graph of the solution of the given inequality$x-9<-4$ that is graph of$x<5$ is:

It can be noticed that at $x=5$, there is open circle because 5 is not included in the inequality $x<5$.