Solve the inequality. Write the solution set in interval notation.
-$$\frac { 2 } { x - 6 }

Question

Solve the inequality. Write the solution set in interval notation.
-$$\frac { 2 } { x - 6 } < 1$$
A) $( - \infty , 6 ) \cup ( 8 , \infty )$
B) $( - \infty , 6 )$
C) $( 6,8 )$
D) $( - \infty , 6 ] \cup [ 8 , \infty )$

Quizplus · Accepted Answer

To solve the inequality $\frac{2}{x-6} < 1$, we first find the common denominator and subtract 1 from both sides to get $\frac{2}{x-6} - \frac{x-6}{x-6} < 0$, which simplifies to $\frac{2-(x-6)}{x-6} < 0$, or $\frac{8-x}{x-6} < 0$. The critical points are x = 6 and x = 8, where the expression is undefined or equals zero. Testing intervals around these points, we find that the inequality is satisfied for $x < 6$ and $x > 8$, leading to the solution set $(-\infty, 6) \cup (8, \infty)$.

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Solve the Inequality $\frac { 2 } { x - 6 } < 1$