Finite Math Examples

$4 x - 6 y (3 x + 17) = 24$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$4 x - 6 y (3 x) - 6 y \cdot 17 = 24$

Step 1.2

Rewrite using the commutative property of multiplication.

$4 x - 6 \cdot 3 y x - 6 y \cdot 17 = 24$

Step 1.3

Multiply $17$ by $- 6$ .

$4 x - 6 \cdot 3 y x - 102 y = 24$

Step 1.4

Multiply $- 6$ by $3$ .

$4 x - 18 y x - 102 y = 24$

Step 2

Add $102 y$ to both sides of the equation.

$4 x - 18 y x = 24 + 102 y$

Step 3

Factor $2 x$ out of $4 x - 18 y x$ .

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Step 3.1

Factor $2 x$ out of $4 x$ .

$2 x (2) - 18 y x = 24 + 102 y$

Step 3.2

Factor $2 x$ out of $- 18 y x$ .

$2 x (2) + 2 x (- 9 y) = 24 + 102 y$

Step 3.3

Factor $2 x$ out of $2 x (2) + 2 x (- 9 y)$ .

$2 x (2 - 9 y) = 24 + 102 y$

Step 4

Divide each term in $2 x (2 - 9 y) = 24 + 102 y$ by $2 (2 - 9 y)$ and simplify.

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Step 4.1

Divide each term in $2 x (2 - 9 y) = 24 + 102 y$ by $2 (2 - 9 y)$ .

$\frac{2 x (2 - 9 y)}{2 (2 - 9 y)} = \frac{24}{2 (2 - 9 y)} + \frac{102 y}{2 (2 - 9 y)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 x (2 - 9 y)}{2 (2 - 9 y)} = \frac{24}{2 (2 - 9 y)} + \frac{102 y}{2 (2 - 9 y)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{x (2 - 9 y)}{2 - 9 y} = \frac{24}{2 (2 - 9 y)} + \frac{102 y}{2 (2 - 9 y)}$

Step 4.2.2

Cancel the common factor of $2 - 9 y$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{x (2 - 9 y)}{2 - 9 y} = \frac{24}{2 (2 - 9 y)} + \frac{102 y}{2 (2 - 9 y)}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{24}{2 (2 - 9 y)} + \frac{102 y}{2 (2 - 9 y)}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $24$ and $2$ .

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Step 4.3.1.1.1

Factor $2$ out of $24$ .

$x = \frac{2 \cdot 12}{2 (2 - 9 y)} + \frac{102 y}{2 (2 - 9 y)}$

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Cancel the common factor.

$x = \frac{2 \cdot 12}{2 (2 - 9 y)} + \frac{102 y}{2 (2 - 9 y)}$

Step 4.3.1.1.2.2

Rewrite the expression.

$x = \frac{12}{2 - 9 y} + \frac{102 y}{2 (2 - 9 y)}$

Step 4.3.1.2

Cancel the common factor of $102$ and $2$ .

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Step 4.3.1.2.1

Factor $2$ out of $102 y$ .

$x = \frac{12}{2 - 9 y} + \frac{2 (51 y)}{2 (2 - 9 y)}$

Step 4.3.1.2.2

Cancel the common factors.

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Step 4.3.1.2.2.1

Cancel the common factor.

$x = \frac{12}{2 - 9 y} + \frac{2 (51 y)}{2 (2 - 9 y)}$

Step 4.3.1.2.2.2

Rewrite the expression.

$x = \frac{12}{2 - 9 y} + \frac{51 y}{2 - 9 y}$

Step 4.3.2

Simplify terms.

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Step 4.3.2.1

Combine the numerators over the common denominator.

$x = \frac{12 + 51 y}{2 - 9 y}$

Step 4.3.2.2

Factor $3$ out of $12 + 51 y$ .

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Step 4.3.2.2.1

Factor $3$ out of $12$ .

$x = \frac{3 (4) + 51 y}{2 - 9 y}$

Step 4.3.2.2.2

Factor $3$ out of $51 y$ .

$x = \frac{3 (4) + 3 (17 y)}{2 - 9 y}$

Step 4.3.2.2.3

Factor $3$ out of $3 (4) + 3 (17 y)$ .

$x = \frac{3 (4 + 17 y)}{2 - 9 y}$