91Ó°ÊÓ

Let the number be $x$. The difference of a number and 4 is $x−4$. The phrase no more than means the same as less than or equal to. Therefore, the inequality is $x−4≤8$

For all numbers $p,q$and $r$, following are true.

(i) If $p>q$, then $p−r>q−r$.

(ii) If $p<q$, then $p−r<q−r$.

Use subtraction property of inequalities to solve the given inequalities.

$\begin{array}{c}x−4≤8\\ x−4+4≤8+4\\ x≤12\end{array}$

Therefore, the solution $x−4≤8$of is $x≤12$.

To check the obtained solution, substitute a number less than as $x≤12$in the inequality $x−4≤8$, if the condition obtained is true, the solution is correct and if the condition obtained is false, the solution is incorrect.

Let $x=10$, as $x=10$. Substitute 10 for $x$into $x−4≤8$.

$\begin{array}{c}x−4≤8\\ 10−4≤8\\ 6≤8\end{array}$

As, the condition obtained$6≤8$ is true, therefore the solution is correct.