91Ó°ÊÓ

The division property of inequalities states that if both sides of the inequality are divided by a positive number the sign of the inequality remains the same and if both sides of the inequality are divided by a negative number then the sign of the inequality changes that is:

1. If $a>b$and$c$ is a positive number then $\frac{a}{c}>\frac{b}{c}$.
2. If $a<b$and$c$ is a positive number then $\frac{a}{c}<\frac{b}{c}$.
3. If$a>b$ and$c$ is a negative number then $\frac{a}{c}<\frac{b}{c}$.
4. If$a<b$ and$c$ is a negative number then $\frac{a}{c}>\frac{b}{c}$.

The solution of the given inequality$7w≤−42$ is:

$\begin{array}{c}7w≤−42\\ \frac{7w}{7}≤\frac{−42}{7}\left(\text{byusingdivisionpropertyofinequality}\right)\\ w≤−6\end{array}$

Therefore, the solution of the given inequality$7w≤−42$ is $w≤−6$.

To perform the check of the solution, substitute a number less than or equal to $−6$as $w≤−6$in the given inequality $7w≤−42$, if the condition obtained is true, the solution is correct and if the condition obtained is false, the solution is incorrect.

Let $w=−7$, as $−7≤−6$.

Now substitute $−7$for $w$in the inequality $7w≤−42$.

$\begin{array}{c}7w≤−42\\ 7\left(−7\right)≤−42\\ −49≤−42\end{array}$

As, the condition obtained$−49≤−42$ is true, therefore the solution is correct.