Pre-Algebra Examples

$t = \frac{7 u}{b + e}$

Step 1

Rewrite the equation as $\frac{7 u}{b + e} = t$ .

$\frac{7 u}{b + e} = t$

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.

$b + e, 1$

Step 2.2

Remove parentheses.

$b + e, 1$

Step 2.3

The LCM of one and any expression is the expression.

$b + e$

Step 3

Multiply each term in $\frac{7 u}{b + e} = t$ by $b + e$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{7 u}{b + e} = t$ by $b + e$ .

$\frac{7 u}{b + e} (b + e) = t (b + e)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $b + e$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7 u}{b + e} (b + e) = t (b + e)$

Step 3.2.1.2

Rewrite the expression.

$7 u = t (b + e)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$7 u = t b + t e$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $t b + t e = 7 u$ .

$t b + t e = 7 u$

Step 4.2

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

$t b = 7 u - t e$

Step 4.3

Divide each term in $t b = 7 u - t e$ by $t$ and simplify.

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Step 4.3.1

Divide each term in $t b = 7 u - t e$ by $t$ .

$\frac{t b}{t} = \frac{7 u}{t} + \frac{- t e}{t}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $t$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{t b}{t} = \frac{7 u}{t} + \frac{- t e}{t}$

Step 4.3.2.1.2

Divide $b$ by $1$ .

$b = \frac{7 u}{t} + \frac{- t e}{t}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Simplify each term.

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Step 4.3.3.1.1

Cancel the common factor of $t$ .

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Step 4.3.3.1.1.1

Cancel the common factor.

$b = \frac{7 u}{t} + \frac{- t e}{t}$

Step 4.3.3.1.1.2

Divide $- 1 e$ by $1$ .

$b = \frac{7 u}{t} - 1 e$

Step 4.3.3.1.2

Rewrite $- 1 e$ as $- e$ .

$b = \frac{7 u}{t} - e$