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:

(i) If $a>b$, then $a−c>b−c$.

(ii) 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:

(i) If $a>b$and role="math" localid="1647496591700" $c$is a positive number then $ac>bc$.

(ii) If $a<b$and$c$is a positive number then $ac<bc$.

(ii) If $a>b$and$c$ is a negative number then $ac<bc$.

(iv) If$a<b$ and$c$ is a negative number then $ac>bc$.

The solution of the given inequality$13−pâ‰\yen 15$ is:

$\begin{array}{l}13−pâ‰\yen 15\\ 13−p−13â‰\yen 15−13\left(\text{byusingsubtractionpropertyofinequality}\right)\\ −p+13−13â‰\yen 2\\ −pâ‰\yen 2\\ (−1)(−p)≤2(−1)\left(\text{byusingmutiplicationpropertyofinequality}\right)\\ p≤−2\end{array}$

Therefore, the solution of the given inequality$13−pâ‰\yen 15$ is $p≤−2$.

The graph of the solution of the given inequality $13−pâ‰\yen 15$that is graph of $p≤−2$is:

It can be noticed that at $p=−2$, there is closed circle because$−2$ is included in the inequality $p≤−2$.