Basic Math Examples

$L = \frac{a - b}{9}$

Step 1

Rewrite the equation as $\frac{a - b}{9} = L$ .

$\frac{a - b}{9} = L$

Step 2

Multiply both sides by $9$ .

$\frac{a - b}{9} \cdot 9 = L \cdot 9$

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 $9$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{a - b}{9} \cdot 9 = L \cdot 9$

Step 3.1.1.2

Rewrite the expression.

$a - b = L \cdot 9$

Step 3.2

Simplify the right side.

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Step 3.2.1

Move $9$ to the left of $L$ .

$a - b = 9 L$

Step 4

Solve for $b$ .

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Step 4.1

Subtract $a$ from both sides of the equation.

$- b = 9 L - a$

Step 4.2

Divide each term in $- b = 9 L - a$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- b = 9 L - a$ by $- 1$ .

$\frac{- b}{- 1} = \frac{9 L}{- 1} + \frac{- a}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{9 L}{- 1} + \frac{- a}{- 1}$

Step 4.2.2.2

Divide $b$ by $1$ .

$b = \frac{9 L}{- 1} + \frac{- a}{- 1}$

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

Move the negative one from the denominator of $\frac{9 L}{- 1}$ .

$b = - 1 \cdot (9 L) + \frac{- a}{- 1}$

Step 4.2.3.1.2

Rewrite $- 1 \cdot (9 L)$ as $- (9 L)$ .

$b = - (9 L) + \frac{- a}{- 1}$

Step 4.2.3.1.3

Multiply $9$ by $- 1$ .

$b = - 9 L + \frac{- a}{- 1}$

Step 4.2.3.1.4

Dividing two negative values results in a positive value.

$b = - 9 L + \frac{a}{1}$

Step 4.2.3.1.5

Divide $a$ by $1$ .

$b = - 9 L + a$