Solve x/3+2<x

$$\frac { x } { 3 } + 2 < x$$

Solve for x

$$x>3$$

Solution Steps

Subtract x from both sides.

$$\frac{x}{3}+2-x<0$$

Combine \frac{x}{3} and -x to get -\frac{2}{3}x.

$$-\frac{2}{3}x+2<0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{2}{3}x<-2$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}. Since -\frac{2}{3} is negative, the inequality direction is changed.

$$x>-2\left(-\frac{3}{2}\right)$$

Multiply -2 times -\frac{3}{2}.

$$x>3$$