Solve the Inequality for x y<2x+1

$y < 2 x + 1$

Step 1

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

$2 x + 1 > y$

Step 2

Subtract $1$ from both sides of the inequality.

$2 x > y - 1$

Step 3

Divide each term in $2 x > y - 1$ by $2$ and simplify.

Divide each term in $2 x > y - 1$ by $2$ .

$\frac{2 x}{2} > \frac{y}{2} + \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{y}{2} + \frac{- 1}{2}$

Divide $x$ by $1$ .

$x > \frac{y}{2} + \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x > \frac{y}{2} - \frac{1}{2}$