Finite Math Examples

f (x, y) \cdot (5 x) + 8 y x + y > 6

$f (x, y) \cdot (5 x) + 8 y x + y > 6$ ,

2 x + 3 y < 18

$2 x + 3 y < 18$ ,

x > 0

$x > 0$ ,

y > 0

$y > 0$

Step 1

Simplify the first inequality.

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Step 1.1

Simplify

f (x, y) \cdot (5 x) + 8 y x + y

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

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Rewrite using the commutative property of multiplication.

5 f (x, y) x + 8 y x + y > 6

$5 f (x, y) x + 8 y x + y > 6$ and

2 x + 3 y < 18

$2 x + 3 y < 18$

Step 1.1.1.2

Multiply

5 f

$5 f$ by each element of the matrix.

(5 f x, 5 f y) x + 8 y x + y > 6

$(5 f x, 5 f y) x + 8 y x + y > 6$ and

2 x + 3 y < 18

$2 x + 3 y < 18$

(5 f x, 5 f y) x + 8 y x + y > 6

$(5 f x, 5 f y) x + 8 y x + y > 6$ and

2 x + 3 y < 18

$2 x + 3 y < 18$

Step 1.1.2

Reorder factors in

(5 f x, 5 f y) x + 8 y x + y

$(5 f x, 5 f y) x + 8 y x + y$ .

x (5 f x, 5 f y) + 8 y x + y > 6

$x (5 f x, 5 f y) + 8 y x + y > 6$ and

2 x + 3 y < 18

$2 x + 3 y < 18$

x (5 f x, 5 f y) + 8 y x + y > 6

$x (5 f x, 5 f y) + 8 y x + y > 6$ and

2 x + 3 y < 18

$2 x + 3 y < 18$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply

x

$x$ by each element of the matrix.

(x (5 f x), x (5 f y)) + 8 y x + y > 6

$(x (5 f x), x (5 f y)) + 8 y x + y > 6$ and

2 x + 3 y < 18

$2 x + 3 y < 18$

Step 1.2.2

Simplify each element in the matrix.

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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

$(5 x (f x), x (5 f y)) + 8 y x + y > 6$ and

$2 x + 3 y < 18$

Step 1.2.2.2

Multiply

$x$ by

$x$ by adding the exponents.

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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

$2 x + 3 y < 18$

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

$2 x + 3 y < 18$

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

$2 x + 3 y < 18$

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

$2 x + 3 y < 18$

Step 1.3

Move all terms not containing

$f$ to the right side of the inequality.

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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

$2 x + 3 y < 18$

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

$2 x + 3 y < 18$

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

$2 x + 3 y < 18$

Step 2

Simplify the second inequality.

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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.

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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.

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Step 2.2.2.1

Cancel the common factor of

$2$ .

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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

$x < \frac{18}{2} + \frac{- 3 y}{2}$

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

$x < \frac{18}{2} + \frac{- 3 y}{2}$

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

$x < \frac{18}{2} + \frac{- 3 y}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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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

$x < 9 - \frac{3 y}{2}$

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

$x < 9 - \frac{3 y}{2}$

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

$x < 9 - \frac{3 y}{2}$

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

$x < 9 - \frac{3 y}{2}$

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

$x < 9 - \frac{3 y}{2}$

Step 3