Algebra Examples

$h = 4 (x + 3 y) + 2$

Step 1

Rewrite the equation as $4 (x + 3 y) + 2 = h$ .

$4 (x + 3 y) + 2 = h$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$4 x + 4 (3 y) + 2 = h$

Step 2.2

Multiply $3$ by $4$ .

$4 x + 12 y + 2 = h$

Step 3

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

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Step 3.1

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

$4 x + 2 = h - 12 y$

Step 3.2

Subtract $2$ from both sides of the equation.

$4 x = h - 12 y - 2$

Step 4

Divide each term in $4 x = h - 12 y - 2$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 x = h - 12 y - 2$ by $4$ .

$\frac{4 x}{4} = \frac{h}{4} + \frac{- 12 y}{4} + \frac{- 2}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{h}{4} + \frac{- 12 y}{4} + \frac{- 2}{4}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{h}{4} + \frac{- 12 y}{4} + \frac{- 2}{4}$

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 $- 12$ and $4$ .

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Step 4.3.1.1.1

Factor $4$ out of $- 12 y$ .

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

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Factor $4$ out of $4$ .

$x = \frac{h}{4} + \frac{4 (- 3 y)}{4 (1)} + \frac{- 2}{4}$

Step 4.3.1.1.2.2

Cancel the common factor.

$x = \frac{h}{4} + \frac{4 (- 3 y)}{4 \cdot 1} + \frac{- 2}{4}$

Step 4.3.1.1.2.3

Rewrite the expression.

$x = \frac{h}{4} + \frac{- 3 y}{1} + \frac{- 2}{4}$

Step 4.3.1.1.2.4

Divide $- 3 y$ by $1$ .

$x = \frac{h}{4} - 3 y + \frac{- 2}{4}$

Step 4.3.1.2

Cancel the common factor of $- 2$ and $4$ .

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Step 4.3.1.2.1

Factor $2$ out of $- 2$ .

$x = \frac{h}{4} - 3 y + \frac{2 (- 1)}{4}$

Step 4.3.1.2.2

Cancel the common factors.

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Step 4.3.1.2.2.1

Factor $2$ out of $4$ .

$x = \frac{h}{4} - 3 y + \frac{2 \cdot - 1}{2 \cdot 2}$

Step 4.3.1.2.2.2

Cancel the common factor.

$x = \frac{h}{4} - 3 y + \frac{2 \cdot - 1}{2 \cdot 2}$

Step 4.3.1.2.2.3

Rewrite the expression.

$x = \frac{h}{4} - 3 y + \frac{- 1}{2}$

Step 4.3.1.3

Move the negative in front of the fraction.

$x = \frac{h}{4} - 3 y - \frac{1}{2}$