Solve the inequality and write the solution set in interval notation. $6 x ^ { 2 } - 10 x

Question

Solve the inequality and write the solution set in interval notation.​ $6 x ^ { 2 } - 10 x < 0$ ​
A) $$( - \infty , 0 ) ] \cup [$$ $\frac { 5 } { 3 }$ $, \infty )$
B) $$\varnothing$$
C) $$( - \infty , 0 )  \cup($$ $\frac { 5 } { 3 }$ $, \infty )$
D) $( \infty , 0 ) \cup [ -$ $\frac { 5 } { 3 }$ $, \infty )$
E) $( 0 ,$ $\frac { 5 } { 3 }$ ) ​

Quizplus · Accepted Answer

First, factor the inequality: $6x^2 - 10x < 0$ can be written as $2x(3x - 5) < 0$. The roots are $x = 0$ and $x = \frac{5}{3}$. The inequality is satisfied for values between these roots, hence the solution is $x \in (0, \frac{5}{3})$.

Solve the Inequality and Write the Solution Set in Interval 6x2−10x<06 x ^ { 2 } - 10 x < 06x2−10x<0

Solve the Inequality and Write the Solution Set in Interval $6 x ^ { 2 } - 10 x < 0$