Solve the problem.
-A number minus the product of 36 and its reciprocal is less than zero. Find the numbers which satisfy this condition.
A) any number less than $- 6$ or between 0 and 6
B) any number between 0 and 6
C) any number between $- 6$ and 6
D) any number less than 6

Question

Quizplus · Accepted Answer

The given inequality can be written as $x - 36\left(\frac{1}{x}\right) < 0$, which simplifies to $x - \frac{36}{x} < 0$. Multiplying both sides by $x$ (assuming $x \neq 0$ to avoid division by zero), we get $x^2 - 36 < 0$, which simplifies to $x^2 < 36$. Taking the square root of both sides gives $-6 < x < 6$, which means any number less than $-6$ or between $0$ and $6$ does not satisfy this inequality directly. However, considering the original inequality and the process of solving it, we see that the solution set includes numbers less than $-6$ and numbers between $0$ and $6$, because these sets of numbers make the original inequality true. The confusion might arise from the direct interpretation of the square root step, but the correct approach is to consider the entire range of values that make the original inequality true, which includes numbers less than $-6$ and numbers greater than $0$ but less than $6$.

Solve the Problem −6- 6−6 Or Between 0 and 6 B) Any Number Between 0

Solve the Problem $- 6$ Or Between 0 and 6
B) Any Number Between 0