Question

Solve the polynomial inequality. Express the solution set in in interval notation: $\frac{8}{x-1}<1$

• A. $(-\infty ,1)$ or $(9,\infty )$
• B. $(-\infty ,1)$
• C. (1, 9)
• D. $(-\infty ,0]$or $[9,\infty )$

Answer 1

The correct option is A $(-\infty ,1)$ or $(9,\infty )$

Given, $\frac{8}{x-1}<1$

$\Rightarrow$ $\frac{8}{x-1}-1<0$

$\Rightarrow$$\frac{9-x}{x-1}<0$

$\Rightarrow$$\frac{x-9}{x-1}>0$

Hence, $x>9$ and $\frac{1}{x-1}>0$

$\Rightarrow$$x<1$ and $x>9$

Hence, the solution is, $(-\infty ,1)$ or $(9,\infty )$