Finite Math Examples

$f (x, y) \cdot (5 x) + 8 y x + y > 6$ , $2 x + 3 y < 18$ , $x > 0$ , $y > 0$

Step 1

Simplify the first inequality.

Tap for more steps...

Step 1.1

Simplify $f (x, y) \cdot (5 x) + 8 y x + y$ .

Tap for more steps...

Step 1.1.1

Simplify each term.

Tap for more steps...

Step 1.1.1.1

Rewrite using the commutative property of multiplication.

$5 f (x, y) x + 8 y x + y > 6$ and $2 x + 3 y < 18$

Step 1.1.1.2

Multiply $5 f$ by each element of the matrix.

$(5 f x, 5 f y) x + 8 y x + y > 6$ and $2 x + 3 y < 18$

Step 1.1.2

Reorder factors in $(5 f x, 5 f y) x + 8 y x + y$ .

$x (5 f x, 5 f y) + 8 y x + y > 6$ and $2 x + 3 y < 18$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Multiply $x$ by each element of the matrix.

$(x (5 f x), x (5 f y)) + 8 y x + y > 6$ and $2 x + 3 y < 18$

Step 1.2.2

Simplify each element in the matrix.

Tap for more steps...

Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$(5 x (f x), x (5 f y)) + 8 y x + y > 6$ and $2 x + 3 y < 18$

Step 1.2.2.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.2.2.2.1

Move $x$ .

$(5 (x \cdot x) f, x (5 f y)) + 8 y x + y > 6$ and $2 x + 3 y < 18$

Step 1.2.2.2.2

Multiply $x$ by $x$ .

$(5 x^{2} f, x (5 f y)) + 8 y x + y > 6$ and $2 x + 3 y < 18$

Step 1.2.2.3

Rewrite using the commutative property of multiplication.

$(5 x^{2} f, 5 x f y) + 8 y x + y > 6$ and $2 x + 3 y < 18$

Step 1.3

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

Tap for more steps...

Step 1.3.1

Subtract $8 y x$ from both sides of the inequality.

$(5 x^{2} f, 5 x f y) + y > 6 - 8 y x$ and $2 x + 3 y < 18$

Step 1.3.2

Subtract $y$ from both sides of the inequality.

$(5 x^{2} f, 5 x f y) > 6 - 8 y x - y$ and $2 x + 3 y < 18$

Step 2

Simplify the second inequality.

Tap for more steps...

Step 2.1

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

$(5 x^{2} f, 5 x f y) > 6 - 8 y x - y$ and $2 x < 18 - 3 y$

Step 2.2

Divide each term in $2 x < 18 - 3 y$ by $2$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $2 x < 18 - 3 y$ by $2$ .

$(5 x^{2} f, 5 x f y) > 6 - 8 y x - y$ and $\frac{2 x}{2} < \frac{18}{2} + \frac{- 3 y}{2}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$(5 x^{2} f, 5 x f y) > 6 - 8 y x - y$ and $\frac{2 x}{2} < \frac{18}{2} + \frac{- 3 y}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$(5 x^{2} f, 5 x f y) > 6 - 8 y x - y$ and $x < \frac{18}{2} + \frac{- 3 y}{2}$

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 $18$ by $2$ .

$(5 x^{2} f, 5 x f y) > 6 - 8 y x - y$ and $x < 9 + \frac{- 3 y}{2}$

Step 2.2.3.1.2

Move the negative in front of the fraction.

$(5 x^{2} f, 5 x f y) > 6 - 8 y x - y$ and $x < 9 - \frac{3 y}{2}$

Step 3