Algebra Examples

$x = \frac{13 (t - 4 y)}{y}$

Step 1

Rewrite the equation as $\frac{13 (t - 4 y)}{y} = x$ .

$\frac{13 (t - 4 y)}{y} = x$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$y, 1$

Step 2.2

The LCM of one and any expression is the expression.

$y$

Step 3

Multiply each term in $\frac{13 (t - 4 y)}{y} = x$ by $y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{13 (t - 4 y)}{y} = x$ by $y$ .

$\frac{13 (t - 4 y)}{y} y = x y$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $y$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{13 (t - 4 y)}{y} y = x y$

Step 3.2.1.2

Rewrite the expression.

$13 (t - 4 y) = x y$

Step 3.2.2

Apply the distributive property.

$13 t + 13 (- 4 y) = x y$

Step 3.2.3

Multiply $- 4$ by $13$ .

$13 t - 52 y = x y$

Step 4

Solve the equation.

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Step 4.1

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

$13 t - 52 y - x y = 0$

Step 4.2

Subtract $13 t$ from both sides of the equation.

$- 52 y - x y = - 13 t$

Step 4.3

Factor $y$ out of $- 52 y - x y$ .

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Step 4.3.1

Factor $y$ out of $- 52 y$ .

$y \cdot - 52 - x y = - 13 t$

Step 4.3.2

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

$y \cdot - 52 + y (- x) = - 13 t$

Step 4.3.3

Factor $y$ out of $y \cdot - 52 + y (- x)$ .

$y (- 52 - x) = - 13 t$

Step 4.4

Divide each term in $y (- 52 - x) = - 13 t$ by $- 52 - x$ and simplify.

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Step 4.4.1

Divide each term in $y (- 52 - x) = - 13 t$ by $- 52 - x$ .

$\frac{y (- 52 - x)}{- 52 - x} = \frac{- 13 t}{- 52 - x}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $- 52 - x$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{y (- 52 - x)}{- 52 - x} = \frac{- 13 t}{- 52 - x}$

Step 4.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 13 t}{- 52 - x}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Move the negative in front of the fraction.

$y = - \frac{13 t}{- 52 - x}$

Step 4.4.3.2

Rewrite $- 52$ as $- 1 (52)$ .

$y = - \frac{13 t}{- 1 (52) - x}$

Step 4.4.3.3

Factor $- 1$ out of $- x$ .

$y = - \frac{13 t}{- 1 (52) - (x)}$

Step 4.4.3.4

Factor $- 1$ out of $- 1 (52) - (x)$ .

$y = - \frac{13 t}{- 1 (52 + x)}$

Step 4.4.3.5

Simplify the expression.

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Step 4.4.3.5.1

Move the negative in front of the fraction.

$y = - - \frac{13 t}{52 + x}$

Step 4.4.3.5.2

Multiply $- 1$ by $- 1$ .

$y = 1 \frac{13 t}{52 + x}$

Step 4.4.3.5.3

Multiply $\frac{13 t}{52 + x}$ by $1$ .

$y = \frac{13 t}{52 + x}$