Question

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

$\mathit{x}\mathbf{+}\mathbf{8}\mathbf{\le }\mathbf{3}$

Short answer

The solution of the given inequality$x+8\le 3$ is $\mathit{x}\mathbf{\le }\mathbf{-}\mathbf{5}$.

The graph of the solution of the given inequality$x+8\le 3$ that is graph of$x\le -5$ 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 x+8≤3.

The solution of the given inequality $x+8\le 3$is:

localid="1647495544907" $\begin{array}{c}x+8\le 3\\ x+8-8\le 3-8\\ x\le -5\end{array}\left(\text{byusingsubtractionpropertyofinequality}\right)$

Therefore, the solution of the given inequality $x+8\le 3$is $x\le -5$.

Step 3. Draw the graph of the inequality x≤−5.

The graph of the solution of the given inequality $x+8\le 3$that is graph of $x\le -5$is:

It can be noticed that at $x=-5$, there is closed circle because$-5$ is included in the inequality $x\le -5$.