Solve the Inequality for x y<3x+1

$y < 3 x + 1$

Rewrite so $x$ is on the left side of the inequality.

$3 x + 1 > y$

Subtract $1$ from both sides of the inequality.

$3 x > y - 1$

Divide each term in $3 x > y - 1$ by $3$ and simplify.

Divide each term in $3 x > y - 1$ by $3$ .

$\frac{3 x}{3} > \frac{y}{3} + \frac{- 1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{y}{3} + \frac{- 1}{3}$

Divide $x$ by $1$ .

$x > \frac{y}{3} + \frac{- 1}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x > \frac{y}{3} - \frac{1}{3}$