91Ó°ÊÓ

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:

1. If $a>b$, then $a−c>b−c$.
2. If $a<b$, then $a−c<b−c$.

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

1. If$a>b$ and$c$ is a positive number then $ac>bc$.
2. If$a<b$ and$c$ is a positive number then $ac<bc$.
3. If$a>b$ and$c$ is a negative number then $ac<bc$.
4. If$a<b$ and$c$ is a negative number then $ac>bc$.

The solution of the given inequality $\frac{g}{4}+3≤−9$is:

$\begin{array}{c}\frac{g}{4}+3≤−9\\ \frac{g}{4}+3−3≤−9−3\left(\text{byusingsubtractionpropertyofinequality}\right)\\ \frac{g}{4}≤−12\\ \left(4\right)\left(\frac{g}{4}\right)≤\left(4\right)\left(−12\right)\left(\text{byusingmultiplicationpropertyofinequality}\right)\\ g≤−48\end{array}$

Therefore, the solution of the given inequality$\frac{g}{4}+3≤−9$ is $g≤−48$.

To perform the check of the solution, substitute a number less than or equal to $−48$as $g≤−48$in the given inequality $\frac{g}{4}+3≤−9$, if the condition obtained is true, the solution is correct and if the condition obtained is false, the solution is incorrect.

Let $g=−52$, as $−52≤−48$.

Now substitute $−52$for $g$in the inequality $\frac{g}{4}+3≤−9$.

$\begin{array}{c}\frac{g}{4}+3≤−9\\ \frac{−52}{4}+3≤−9\\ −13+3≤−9\\ −10≤−9\end{array}$

As, the condition obtained$−10≤−9$ is true, therefore the solution is correct.