To solve the inequality [tex]\(81 - 1 \frac{1}{5} x \leq 55\)[/tex], let's follow a step-by-step process:
1. Rewrite the Inequality:
The inequality can be rewritten to make it easier to solve. Notice that [tex]\(1 \frac{1}{5}\)[/tex] is equivalent to [tex]\(1 + \frac{1}{5}\)[/tex] or [tex]\(\frac{6}{5}\)[/tex].
Therefore, the inequality is:
[tex]\[
81 - \frac{6}{5} x \leq 55
\][/tex]
2. Isolate the [tex]\(x\)[/tex] Term:
To isolate the [tex]\(x\)[/tex] term, subtract 81 from both sides of the inequality.
[tex]\[
81 - \frac{6}{5} x - 81 \leq 55 - 81
\][/tex]
Simplify the terms:
[tex]\[
-\frac{6}{5} x \leq -26
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Next, solve for [tex]\(x\)[/tex] by dividing both sides of the inequality by [tex]\(-\frac{6}{5}\)[/tex]. Remember, when dividing by a negative number, the direction of the inequality sign flips.
[tex]\[
x \geq \frac{-26}{-\frac{6}{5}}
\][/tex]
4. Simplify the Fraction:
Simplify the fraction [tex]\(\frac{-26}{-\frac{6}{5}}\)[/tex]:
[tex]\[
x \geq \frac{26}{\frac{6}{5}}
\][/tex]
To divide by a fraction, multiply by its reciprocal:
[tex]\[
x \geq 26 \times \frac{5}{6}
\][/tex]
Simplify the multiplication:
[tex]\[
x \geq \frac{130}{6}
\][/tex]
Further simplify the fraction:
[tex]\[
x \geq 21 \frac{2}{3}
\][/tex]
Therefore, the solution to the inequality [tex]\(81 - 1 \frac{1}{5} x \leq 55\)[/tex] is [tex]\(x \geq 21 \frac{2}{3}\)[/tex].
The correct option is: A. [tex]\(x \geq 21 \frac{2}{3}\)[/tex]
