Solve the System of Inequalities x+2y>=4 3x-2y<4

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

Solve $x + 2 y \geq 4$ for $y$ .

Subtract $x$ from both sides of the inequality.

$2 y \geq 4 - x$

Divide each term in $2 y \geq 4 - x$ by $2$ and simplify.

Divide each term in $2 y \geq 4 - x$ by $2$ .

$\frac{2 y}{2} \geq \frac{4}{2} + \frac{- x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \geq \frac{4}{2} + \frac{- x}{2}$

Divide $y$ by $1$ .

$y \geq \frac{4}{2} + \frac{- x}{2}$

Simplify the right side.

Simplify each term.

Divide $4$ by $2$ .

$y \geq 2 + \frac{- x}{2}$

Move the negative in front of the fraction.

$y \geq 2 - \frac{x}{2}$

Solve $3 x - 2 y < 4$ for $y$ .

Subtract $3 x$ from both sides of the inequality.

$- 2 y < 4 - 3 x$

Divide each term in $- 2 y < 4 - 3 x$ by $- 2$ and simplify.

Divide each term in $- 2 y < 4 - 3 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} > \frac{4}{- 2} + \frac{- 3 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} > \frac{4}{- 2} + \frac{- 3 x}{- 2}$

Divide $y$ by $1$ .

$y > \frac{4}{- 2} + \frac{- 3 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $4$ by $- 2$ .

$y > - 2 + \frac{- 3 x}{- 2}$

Dividing two negative values results in a positive value.

$y > - 2 + \frac{3 x}{2}$

Find the intersection of $y \geq 2 - \frac{x}{2}$ and $y > - 2 + \frac{3 x}{2}$ .

$y \geq 2 - \frac{x}{2}$ and $y > - 2 + \frac{3 x}{2}$

Solve the System of Inequalities x+2y>=4 3x-2y<4

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