Question

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

$\mathit{y}\mathbf{+}\mathbf{1}\mathbf{\le }\mathbf{8}$

Short answer

The solution of the given inequality $y+1\le 8$is role="math" localid="1647497248186" $\mathit{y}\mathbf{\le }\mathbf{7}$.

The graph of the solution of the given inequality $y+1\le 8$that is graph of$y\le 7$ 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 y+1≤8.

The solution of the given inequality $y+1\le 8$is:

$\begin{array}{l}y+1\le 8\\ y+1-1\le 8-1\left(\text{byusingsubtractionpropertyofinequality}\right)\\ y\le 7\end{array}$

Therefore, the solution of the given inequality$y+1\le 8$ is $y\le 7$.

Step 3. Draw the graph of the inequality y≤7.

The graph of the solution of the given inequality$y+1\le 8$ that is graph of$y\le 7$ is:

It can be noticed that at $y=7$, there is closed circle because 7 is included in the inequality $y\le 7$.