Algebra Examples

$- 6 = 3 x - 6 y \cdot 4 x - 4 + 5 y$

Step 1

Rewrite the equation as $3 x - 6 y \cdot (4 x) - 4 + 5 y = - 6$ .

$3 x - 6 y \cdot (4 x) - 4 + 5 y = - 6$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$3 x - 6 \cdot 4 y x - 4 + 5 y = - 6$

Step 2.2

Multiply $- 6$ by $4$ .

$3 x - 24 y x - 4 + 5 y = - 6$

Step 3

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

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Step 3.1

Add $4$ to both sides of the equation.

$3 x - 24 y x + 5 y = - 6 + 4$

Step 3.2

Subtract $5 y$ from both sides of the equation.

$3 x - 24 y x = - 6 + 4 - 5 y$

Step 3.3

Add $- 6$ and $4$ .

$3 x - 24 y x = - 2 - 5 y$

Step 4

Factor $3 x$ out of $3 x - 24 y x$ .

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Step 4.1

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

$3 x (1) - 24 y x = - 2 - 5 y$

Step 4.2

Factor $3 x$ out of $- 24 y x$ .

$3 x (1) + 3 x (- 8 y) = - 2 - 5 y$

Step 4.3

Factor $3 x$ out of $3 x (1) + 3 x (- 8 y)$ .

$3 x (1 - 8 y) = - 2 - 5 y$

Step 5

Divide each term in $3 x (1 - 8 y) = - 2 - 5 y$ by $3 (1 - 8 y)$ and simplify.

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Step 5.1

Divide each term in $3 x (1 - 8 y) = - 2 - 5 y$ by $3 (1 - 8 y)$ .

$\frac{3 x (1 - 8 y)}{3 (1 - 8 y)} = \frac{- 2}{3 (1 - 8 y)} + \frac{- 5 y}{3 (1 - 8 y)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 x (1 - 8 y)}{3 (1 - 8 y)} = \frac{- 2}{3 (1 - 8 y)} + \frac{- 5 y}{3 (1 - 8 y)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{x (1 - 8 y)}{1 - 8 y} = \frac{- 2}{3 (1 - 8 y)} + \frac{- 5 y}{3 (1 - 8 y)}$

Step 5.2.2

Cancel the common factor of $1 - 8 y$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{x (1 - 8 y)}{1 - 8 y} = \frac{- 2}{3 (1 - 8 y)} + \frac{- 5 y}{3 (1 - 8 y)}$

Step 5.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 2}{3 (1 - 8 y)} + \frac{- 5 y}{3 (1 - 8 y)}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Move the negative in front of the fraction.

$x = - \frac{2}{3 (1 - 8 y)} + \frac{- 5 y}{3 (1 - 8 y)}$

Step 5.3.1.2

Move the negative in front of the fraction.

$x = - \frac{2}{3 (1 - 8 y)} - \frac{5 y}{3 (1 - 8 y)}$