Solve the Inequality for x 3x+4y<x-y+2

$3 x + 4 y < x - y + 2$

Step 1

Move all terms containing $x$ to the left side of the inequality.

Subtract $x$ from both sides of the inequality.

$3 x + 4 y - x < - y + 2$

Subtract $x$ from $3 x$ .

$2 x + 4 y < - y + 2$

Step 2

Move all terms not containing $x$ to the right side of the inequality.

Subtract $4 y$ from both sides of the inequality.

$2 x < - y + 2 - 4 y$

Subtract $4 y$ from $- y$ .

$2 x < - 5 y + 2$

Step 3

Divide each term in $2 x < - 5 y + 2$ by $2$ and simplify.

Divide each term in $2 x < - 5 y + 2$ by $2$ .

$\frac{2 x}{2} < \frac{- 5 y}{2} + \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{- 5 y}{2} + \frac{2}{2}$

Divide $x$ by $1$ .

$x < \frac{- 5 y}{2} + \frac{2}{2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x < - \frac{(5) y}{2} + \frac{2}{2}$

Divide $2$ by $2$ .

$x < - \frac{5 y}{2} + 1$