Basic Math Examples

$L = \frac{c + 8 d}{4}$

Step 1

Rewrite the equation as $\frac{c + 8 d}{4} = L$ .

$\frac{c + 8 d}{4} = L$

Step 2

Multiply both sides by $4$ .

$\frac{c + 8 d}{4} \cdot 4 = L \cdot 4$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{c + 8 d}{4} \cdot 4 = L \cdot 4$

Step 3.1.1.2

Rewrite the expression.

$c + 8 d = L \cdot 4$

$c + 8 d = L \cdot 4$

$c + 8 d = L \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Move $4$ to the left of $L$ .

$c + 8 d = 4 L$

$c + 8 d = 4 L$

$c + 8 d = 4 L$

Step 4

Solve for $d$ .

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Step 4.1

Subtract $c$ from both sides of the equation.

$8 d = 4 L - c$

Step 4.2

Divide each term in $8 d = 4 L - c$ by $8$ and simplify.

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Step 4.2.1

Divide each term in $8 d = 4 L - c$ by $8$ .

$\frac{8 d}{8} = \frac{4 L}{8} + \frac{- c}{8}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $8$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{8 d}{8} = \frac{4 L}{8} + \frac{- c}{8}$

Step 4.2.2.1.2

Divide $d$ by $1$ .

$d = \frac{4 L}{8} + \frac{- c}{8}$

$d = \frac{4 L}{8} + \frac{- c}{8}$

$d = \frac{4 L}{8} + \frac{- c}{8}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify each term.

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Step 4.2.3.1.1

Cancel the common factor of $4$ and $8$ .

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Step 4.2.3.1.1.1

Factor $4$ out of $4 L$ .

$d = \frac{4 (L)}{8} + \frac{- c}{8}$

Step 4.2.3.1.1.2

Cancel the common factors.

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Step 4.2.3.1.1.2.1

Factor $4$ out of $8$ .

$d = \frac{4 L}{4 \cdot 2} + \frac{- c}{8}$

Step 4.2.3.1.1.2.2

Cancel the common factor.

$d = \frac{4 L}{4 \cdot 2} + \frac{- c}{8}$

Step 4.2.3.1.1.2.3

Rewrite the expression.

$d = \frac{L}{2} + \frac{- c}{8}$

$d = \frac{L}{2} + \frac{- c}{8}$

$d = \frac{L}{2} + \frac{- c}{8}$

Step 4.2.3.1.2

Move the negative in front of the fraction.

$d = \frac{L}{2} - \frac{c}{8}$

$d = \frac{L}{2} - \frac{c}{8}$

$d = \frac{L}{2} - \frac{c}{8}$

$d = \frac{L}{2} - \frac{c}{8}$

$d = \frac{L}{2} - \frac{c}{8}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$