Pre-Algebra Examples

$\frac{520}{210 + x} = \frac{320}{210 - x}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$520 (210 - x) = (210 + x) \cdot 320$

Step 2

Solve the equation for $x$ .

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Step 2.1

Simplify $520 (210 - x)$ .

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Step 2.1.1

Rewrite.

$0 + 0 + 520 (210 - x) = (210 + x) \cdot 320$

Step 2.1.2

Simplify by adding zeros.

$520 (210 - x) = (210 + x) \cdot 320$

Step 2.1.3

Apply the distributive property.

$520 \cdot 210 + 520 (- x) = (210 + x) \cdot 320$

Step 2.1.4

Multiply.

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Step 2.1.4.1

Multiply $520$ by $210$ .

$109200 + 520 (- x) = (210 + x) \cdot 320$

Step 2.1.4.2

Multiply $- 1$ by $520$ .

$109200 - 520 x = (210 + x) \cdot 320$

Step 2.2

Simplify $(210 + x) \cdot 320$ .

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Step 2.2.1

Apply the distributive property.

$109200 - 520 x = 210 \cdot 320 + x \cdot 320$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Multiply $210$ by $320$ .

$109200 - 520 x = 67200 + x \cdot 320$

Step 2.2.2.2

Move $320$ to the left of $x$ .

$109200 - 520 x = 67200 + 320 x$

Step 2.3

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

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Step 2.3.1

Subtract $320 x$ from both sides of the equation.

$109200 - 520 x - 320 x = 67200$

Step 2.3.2

Subtract $320 x$ from $- 520 x$ .

$109200 - 840 x = 67200$

Step 2.4

Move all terms not containing $x$ to the right side of the equation.

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Step 2.4.1

Subtract $109200$ from both sides of the equation.

$- 840 x = 67200 - 109200$

Step 2.4.2

Subtract $109200$ from $67200$ .

$- 840 x = - 42000$

Step 2.5

Divide each term in $- 840 x = - 42000$ by $- 840$ and simplify.

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Step 2.5.1

Divide each term in $- 840 x = - 42000$ by $- 840$ .

$\frac{- 840 x}{- 840} = \frac{- 42000}{- 840}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $- 840$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{- 840 x}{- 840} = \frac{- 42000}{- 840}$

Step 2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 42000}{- 840}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Divide $- 42000$ by $- 840$ .

$x = 50$