Algebra Examples

$0 = 3 x - 16 + 2 y \frac{15}{2} - 3 y + \frac{27}{8} x$

Step 1

Rewrite the equation as $3 x - 16 + 2 y (\frac{15}{2}) - 3 y + \frac{27}{8} x = 0$ .

$3 x - 16 + 2 y (\frac{15}{2}) - 3 y + \frac{27}{8} x = 0$

Step 2

Simplify $3 x - 16 + 2 y (\frac{15}{2}) - 3 y + \frac{27}{8} x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Factor $2$ out of $2 y$ .

$3 x - 16 + 2 (y) \frac{15}{2} - 3 y + \frac{27}{8} x = 0$

Step 2.1.1.2

Cancel the common factor.

$3 x - 16 + 2 y \frac{15}{2} - 3 y + \frac{27}{8} x = 0$

Step 2.1.1.3

Rewrite the expression.

$3 x - 16 + y \cdot 15 - 3 y + \frac{27}{8} x = 0$

Step 2.1.2

Move $15$ to the left of $y$ .

$3 x - 16 + 15 \cdot y - 3 y + \frac{27}{8} x = 0$

Step 2.1.3

Combine $\frac{27}{8}$ and $x$ .

$3 x - 16 + 15 y - 3 y + \frac{27 x}{8} = 0$

Step 2.2

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- 16 + 15 y - 3 y + 3 x \cdot \frac{8}{8} + \frac{27 x}{8} = 0$

Step 2.3

Simplify terms.

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Step 2.3.1

Combine $3 x$ and $\frac{8}{8}$ .

$- 16 + 15 y - 3 y + \frac{3 x \cdot 8}{8} + \frac{27 x}{8} = 0$

Step 2.3.2

Combine the numerators over the common denominator.

$- 16 + 15 y - 3 y + \frac{3 x \cdot 8 + 27 x}{8} = 0$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Factor $3 x$ out of $3 x \cdot 8 + 27 x$ .

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Step 2.4.1.1

Factor $3 x$ out of $3 x \cdot 8$ .

$- 16 + 15 y - 3 y + \frac{3 x (8) + 27 x}{8} = 0$

Step 2.4.1.2

Factor $3 x$ out of $27 x$ .

$- 16 + 15 y - 3 y + \frac{3 x (8) + 3 x (9)}{8} = 0$

Step 2.4.1.3

Factor $3 x$ out of $3 x (8) + 3 x (9)$ .

$- 16 + 15 y - 3 y + \frac{3 x (8 + 9)}{8} = 0$

Step 2.4.2

Add $8$ and $9$ .

$- 16 + 15 y - 3 y + \frac{3 x \cdot 17}{8} = 0$

Step 2.4.3

Multiply $17$ by $3$ .

$- 16 + 15 y - 3 y + \frac{51 x}{8} = 0$

Step 2.5

Subtract $3 y$ from $15 y$ .

$- 16 + 12 y + \frac{51 x}{8} = 0$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Add $16$ to both sides of the equation.

$12 y + \frac{51 x}{8} = 16$

Step 3.2

Subtract $12 y$ from both sides of the equation.

$\frac{51 x}{8} = 16 - 12 y$

Step 4

Multiply both sides of the equation by $\frac{8}{51}$ .

$\frac{8}{51} \cdot \frac{51 x}{8} = \frac{8}{51} (16 - 12 y)$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{8}{51} \cdot \frac{51 x}{8}$ .

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Step 5.1.1.1

Cancel the common factor of $8$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{8}{51} \cdot \frac{51 x}{8} = \frac{8}{51} (16 - 12 y)$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{51} (51 x) = \frac{8}{51} (16 - 12 y)$

Step 5.1.1.2

Cancel the common factor of $51$ .

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Step 5.1.1.2.1

Factor $51$ out of $51 x$ .

$\frac{1}{51} (51 (x)) = \frac{8}{51} (16 - 12 y)$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{51} (51 x) = \frac{8}{51} (16 - 12 y)$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{8}{51} (16 - 12 y)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{8}{51} (16 - 12 y)$ .

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Step 5.2.1.1

Apply the distributive property.

$x = \frac{8}{51} \cdot 16 + \frac{8}{51} (- 12 y)$

Step 5.2.1.2

Multiply $\frac{8}{51} \cdot 16$ .

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Step 5.2.1.2.1

Combine $\frac{8}{51}$ and $16$ .

$x = \frac{8 \cdot 16}{51} + \frac{8}{51} (- 12 y)$

Step 5.2.1.2.2

Multiply $8$ by $16$ .

$x = \frac{128}{51} + \frac{8}{51} (- 12 y)$

Step 5.2.1.3

Cancel the common factor of $3$ .

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Step 5.2.1.3.1

Factor $3$ out of $51$ .

$x = \frac{128}{51} + \frac{8}{3 (17)} (- 12 y)$

Step 5.2.1.3.2

Factor $3$ out of $- 12 y$ .

$x = \frac{128}{51} + \frac{8}{3 (17)} (3 (- 4 y))$

Step 5.2.1.3.3

Cancel the common factor.

$x = \frac{128}{51} + \frac{8}{3 \cdot 17} (3 (- 4 y))$

Step 5.2.1.3.4

Rewrite the expression.

$x = \frac{128}{51} + \frac{8}{17} (- 4 y)$

Step 5.2.1.4

Combine $- 4$ and $\frac{8}{17}$ .

$x = \frac{128}{51} + \frac{- 4 \cdot 8}{17} y$

Step 5.2.1.5

Multiply $- 4$ by $8$ .

$x = \frac{128}{51} + \frac{- 32}{17} y$

Step 5.2.1.6

Combine $\frac{- 32}{17}$ and $y$ .

$x = \frac{128}{51} + \frac{- 32 y}{17}$

Step 5.2.1.7

Move the negative in front of the fraction.

$x = \frac{128}{51} - \frac{32 y}{17}$

Step 6

Reorder $\frac{128}{51}$ and $- \frac{32 y}{17}$ .

$x = - \frac{32 y}{17} + \frac{128}{51}$