Solve the System of Inequalities 3x+4y<28 x-2y<=0

$3 x + 4 y < 28$ $x - 2 y \leq 0$

Solve $3 x + 4 y < 28$ for $y$ .

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

$4 y < 28 - 3 x$

Divide each term in $4 y < 28 - 3 x$ by $4$ and simplify.

Divide each term in $4 y < 28 - 3 x$ by $4$ .

$\frac{4 y}{4} < \frac{28}{4} + \frac{- 3 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} < \frac{28}{4} + \frac{- 3 x}{4}$

Divide $y$ by $1$ .

$y < \frac{28}{4} + \frac{- 3 x}{4}$

Simplify the right side.

Simplify each term.

Divide $28$ by $4$ .

$y < 7 + \frac{- 3 x}{4}$

Move the negative in front of the fraction.

$y < 7 - \frac{3 x}{4}$

Solve $x - 2 y \leq 0$ for $y$ .

Subtract $x$ from both sides of the inequality.

$- 2 y \leq - x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

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

Find the intersection of $y < 7 - \frac{3 x}{4}$ and $y \geq \frac{x}{2}$ .

$\frac{x}{2} \leq y < 7 - \frac{3 x}{4}$

Solve the System of Inequalities 3x+4y<28 x-2y<=0

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