Question

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

$\mathbf{6}\mathbf{+}\mathit{h}\mathbf{<}\mathbf{1}$

Short answer

The solution of the given inequality$6+h<1$ is $\mathit{h}\mathbf{<}\mathbf{-}\mathbf{5}$.

The graph of the solution of the given inequality$6+h<1$ that is graph of$h<-5$ is:

Step-by-step solution

Step 1. Write the subtraction property of inequalities.

The subtraction property of inequalities states that if the same number is subtracted from each side of a true inequality, the resulting inequality is also true that is:

(i) If $a>b$, then $a-c>b-c$.

(ii) If $a<b$, then $a-c<b-c$.

Step 2. Solve the given inequality 6+h<1.

The solution of the given inequality$6+h<1$is:

localid="1647495432794" $\begin{array}{c}6+h<1\\ 6+h-6<1-6\\ h+6-6<-5\\ h<-5\end{array}\left(\text{byusingsubtractionpropertyofinequality}\right)$

Therefore, the solution of the given inequality$6+h<1$is $h<-5$.

Step 3. Draw the graph of the inequality h<−5.

The graph of the solution of the given inequality$6+h<1$that is graph of$h<-5$is:

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