Question

Solve the polynomial inequality. Express the solution set in in interval notation: $\frac{x+26}{x+5}<5$

• A. $(\infty ,-5)$ or $(\frac{1}{4},\infty )$
• B. $(-5,\frac{1}{4})$
• C. $\varnothing$
• D. $(-\infty ,\frac{1}{4})$ or $(5,\infty )$

Answer 1

The correct option is A $(\infty ,-5)$ or $(\frac{1}{4},\infty )$

Given, $\frac{x+26}{x+5}<5$

$\Rightarrow$ $\frac{x+26}{x+5}-5<0$

$\Rightarrow$$\frac{-4x+1}{x+5}<0$

$\Rightarrow$$x+5>0$

$\Rightarrow$$x>-5$ And $x>\frac{1}{4}$

Hence, solution is, $(\infty ,-5)$ or $(\frac{1}{4},\infty )$