Pre-Algebra Examples

$\frac{5}{1} = \frac{x}{312 - x}$

Step 1

Rewrite the equation as $\frac{x}{312 - x} = \frac{5}{1}$ .

$\frac{x}{312 - x} = \frac{5}{1}$

Step 2

Divide $5$ by $1$ .

$\frac{x}{312 - x} = 5$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

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

$312 - x, 1$

Step 3.2

Remove parentheses.

$312 - x, 1$

Step 3.3

The LCM of one and any expression is the expression.

$312 - x$

Step 4

Multiply each term in $\frac{x}{312 - x} = 5$ by $312 - x$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{x}{312 - x} = 5$ by $312 - x$ .

$\frac{x}{312 - x} (312 - x) = 5 (312 - x)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $312 - x$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x}{312 - x} (312 - x) = 5 (312 - x)$

Step 4.2.1.2

Rewrite the expression.

$x = 5 (312 - x)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Apply the distributive property.

$x = 5 \cdot 312 + 5 (- x)$

Step 4.3.2

Multiply.

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Step 4.3.2.1

Multiply $5$ by $312$ .

$x = 1560 + 5 (- x)$

Step 4.3.2.2

Multiply $- 1$ by $5$ .

$x = 1560 - 5 x$

Step 5

Solve the equation.

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Step 5.1

Move all terms containing $x$ to the left side of the equation.

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Step 5.1.1

Add $5 x$ to both sides of the equation.

$x + 5 x = 1560$

Step 5.1.2

Add $x$ and $5 x$ .

$6 x = 1560$

Step 5.2

Divide each term in $6 x = 1560$ by $6$ and simplify.

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Step 5.2.1

Divide each term in $6 x = 1560$ by $6$ .

$\frac{6 x}{6} = \frac{1560}{6}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $6$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{1560}{6}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1560}{6}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $1560$ by $6$ .

$x = 260$