Q11. - Algebra 1

Question

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

$\mathit{w}\mathbf{-}\mathbf{4}\mathbf{>}\mathbf{9}$

Step-by-Step Solution

Answer

The solution of the given inequality $w-4>9$ is $\mathit{w}\mathbf{>}\mathbf{13}$.

The graph of the solution of the given inequality $w-4>9$ that is graph $w>13$ of is:

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:

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

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

Step 2. Solve the given inequality w &#8722; 4 &#62; 9 .

The solution of the given inequality $w-4>9$ is:

$\begin{array}{c}w-4>9\\ w-4+4>9+4\\ w>13\end{array}\left(\text{by using addition property of inequality}\right)$

Therefore, the solution of the given inequality $w-4>9$ is $w>13$.

Step 3. Draw the graph of the inequality.

The graph of the solution of the given inequality $w-4>9$ that is graph of $w>13$ is:

It can be noticed that at $w=13$, there is open circle because 13 is not included in the inequality $w>13$.