Algebra Examples

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

Step 1

Simplify $3 y - 5 + 4 (x - y)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Multiply $- 1$ by $4$ .

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

Step 1.2

Subtract $4 y$ from $3 y$ .

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

Step 2

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

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Step 2.1

Add $5$ to both sides of the equation.

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

Step 2.2

Subtract $4 x$ from both sides of the equation.

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

Step 2.3

Subtract $4 x$ from $6 x$ .

$- y = 2 x + 5$

Step 3

Divide each term in $- y = 2 x + 5$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = 2 x + 5$ by $- 1$ .

$\frac{- y}{- 1} = \frac{2 x}{- 1} + \frac{5}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{2 x}{- 1} + \frac{5}{- 1}$

Step 3.2.2

Divide $y$ by $1$ .

$y = \frac{2 x}{- 1} + \frac{5}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

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

Step 3.3.1.2

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

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

Step 3.3.1.3

Multiply $2$ by $- 1$ .

$y = - 2 x + \frac{5}{- 1}$

Step 3.3.1.4

Divide $5$ by $- 1$ .

$y = - 2 x - 5$

Step 4