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 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:

(i) If$a>b$ and c is a positive number then $\frac{a}{c}>\frac{b}{c}$.

(ii) If$a<b$ and c is a positive number then $\frac{a}{c}<\frac{b}{c}$.

(iii) If$a>b$ and c is a negative number then $\frac{a}{c}<\frac{b}{c}$.

(iv) If$a<b$ and c is a negative number then $\frac{a}{c}>\frac{b}{c}$.

The solution of the given inequality$18≤−2x+8$ is:

$$\begin{gathered} 18≤−2x+8 \\ 18−8≤−2x+8−8\left(\text{byusingsubtractionpropertyofinequality}\right) \\ 10≤−2x \\ \frac{10}{−2}â‰\yen \frac{−2x}{−2}\left(\text{byusingdivisionpropertyofinequality}\right) \\ −5â‰\yen x \\ x≤−5 \end{gathered}$$

Therefore, the solution of the given inequality$18≤−2x+8$ is $x≤−5$.

To perform the check of the solution, substitute a number less than or equal to$−5$ as$x≤−5$ in the given inequality $18≤−2x+8$, if the condition obtained is true, the solution is correct and if the condition obtained is false, the solution is incorrect.

Let $x=−6$, as $−6≤−5$.

Now substitute$-6$ for x in the inequality $18≤−2x+8$.

$$\begin{gathered} 18≤−2x+8 \\ 18≤−2\left(−6\right)+8 \\ 18≤12+8 \\ 18≤20 \end{gathered}$$

As, the condition obtained$18≤20$ is true, therefore the solution is correct.