Solve and write solution set in interval notation: $\frac { x } { 3 } - \frac { 1 } { 4 }

Question

Solve and write solution set in interval notation: $\frac { x } { 3 } - \frac { 1 } { 4 } < 2 x$
A) $\left( - \infty , - \frac { 3 } { 20 } \right)$
B) $\left( - \frac { 3 } { 20 } , \infty \right)$
C) $( - 3 , \infty )$
D) $( - \infty , - 3 )$

Quizplus · Accepted Answer

First, solve the inequality: $\frac{x}{3} - \frac{1}{4} < 2x$. Subtract $\frac{x}{3}$ from both sides to get $-\frac{1}{4} < \frac{5x}{3}$. Multiply both sides by 3 to get $-\frac{3}{4} < 5x$. Divide by 5 to get $-\frac{3}{20} < x$. This translates to $x > -\frac{3}{20}$, which in interval notation is $\left( - \frac { 3 } { 20 } , \infty \right)$.

Solve and Write Solution Set in Interval Notation x3−14<2x\frac { x } { 3 } - \frac { 1 } { 4 } < 2 x3x​−41​<2x

Solve and Write Solution Set in Interval Notation $\frac { x } { 3 } - \frac { 1 } { 4 } < 2 x$