Finite Math Examples

$3 x + 4 y > 24$ , $4 x + 5 y < 20$ , $x > 0$

Step 1

Solve $3 x + 4 y > 24$ for $y$ .

Tap for more steps...

Step 1.1

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

$4 y > 24 - 3 x$

Step 1.2

Divide each term in $4 y > 24 - 3 x$ by $4$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $4 y > 24 - 3 x$ by $4$ .

$\frac{4 y}{4} > \frac{24}{4} + \frac{- 3 x}{4}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} > \frac{24}{4} + \frac{- 3 x}{4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{24}{4} + \frac{- 3 x}{4}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Divide $24$ by $4$ .

$y > 6 + \frac{- 3 x}{4}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y > 6 - \frac{3 x}{4}$

Step 2

Solve $4 x + 5 y < 20$ for $y$ .

Tap for more steps...

Step 2.1

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

$5 y < 20 - 4 x$

Step 2.2

Divide each term in $5 y < 20 - 4 x$ by $5$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $5 y < 20 - 4 x$ by $5$ .

$\frac{5 y}{5} < \frac{20}{5} + \frac{- 4 x}{5}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} < \frac{20}{5} + \frac{- 4 x}{5}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{20}{5} + \frac{- 4 x}{5}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Simplify each term.

Tap for more steps...

Step 2.2.3.1.1

Divide $20$ by $5$ .

$y < 4 + \frac{- 4 x}{5}$

Step 2.2.3.1.2

Move the negative in front of the fraction.

$y < 4 - \frac{4 x}{5}$

Step 3

Find the intersection of $y > 6 - \frac{3 x}{4}$ and $y < 4 - \frac{4 x}{5}$ .

No solution