Algebra Examples

$\frac{12}{2 - x} = \frac{15}{7 + x}$

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.

$12 (7 + x) = (2 - x) \cdot 15$

Step 2

Solve the equation for $x$ .

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Step 2.1

Simplify $12 (7 + x)$ .

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Step 2.1.1

Rewrite.

$0 + 0 + 12 (7 + x) = (2 - x) \cdot 15$

Step 2.1.2

Simplify by adding zeros.

$12 (7 + x) = (2 - x) \cdot 15$

Step 2.1.3

Apply the distributive property.

$12 \cdot 7 + 12 x = (2 - x) \cdot 15$

Step 2.1.4

Multiply $12$ by $7$ .

$84 + 12 x = (2 - x) \cdot 15$

Step 2.2

Simplify $(2 - x) \cdot 15$ .

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Step 2.2.1

Apply the distributive property.

$84 + 12 x = 2 \cdot 15 - x \cdot 15$

Step 2.2.2

Multiply.

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Step 2.2.2.1

Multiply $2$ by $15$ .

$84 + 12 x = 30 - x \cdot 15$

Step 2.2.2.2

Multiply $15$ by $- 1$ .

$84 + 12 x = 30 - 15 x$

Step 2.3

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

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Step 2.3.1

Add $15 x$ to both sides of the equation.

$84 + 12 x + 15 x = 30$

Step 2.3.2

Add $12 x$ and $15 x$ .

$84 + 27 x = 30$

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 $84$ from both sides of the equation.

$27 x = 30 - 84$

Step 2.4.2

Subtract $84$ from $30$ .

$27 x = - 54$

Step 2.5

Divide each term in $27 x = - 54$ by $27$ and simplify.

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Step 2.5.1

Divide each term in $27 x = - 54$ by $27$ .

$\frac{27 x}{27} = \frac{- 54}{27}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $27$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{27 x}{27} = \frac{- 54}{27}$

Step 2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 54}{27}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Divide $- 54$ by $27$ .

$x = - 2$