Algebra Examples

$\frac{10}{2 x - 9} = \frac{20}{9}$

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.

$10 \cdot 9 = (2 x - 9) \cdot 20$

Step 2

Solve the equation for $x$ .

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Step 2.1

Rewrite the equation as $(2 x - 9) \cdot 20 = 10 \cdot 9$ .

$(2 x - 9) \cdot 20 = 10 \cdot 9$

Step 2.2

Multiply $10$ by $9$ .

$(2 x - 9) \cdot 20 = 90$

Step 2.3

Divide each term in $(2 x - 9) \cdot 20 = 90$ by $20$ and simplify.

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Step 2.3.1

Divide each term in $(2 x - 9) \cdot 20 = 90$ by $20$ .

$\frac{(2 x - 9) \cdot 20}{20} = \frac{90}{20}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $20$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{(2 x - 9) \cdot 20}{20} = \frac{90}{20}$

Step 2.3.2.1.2

Divide $2 x - 9$ by $1$ .

$2 x - 9 = \frac{90}{20}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Cancel the common factor of $90$ and $20$ .

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Step 2.3.3.1.1

Factor $10$ out of $90$ .

$2 x - 9 = \frac{10 (9)}{20}$

Step 2.3.3.1.2

Cancel the common factors.

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Step 2.3.3.1.2.1

Factor $10$ out of $20$ .

$2 x - 9 = \frac{10 \cdot 9}{10 \cdot 2}$

Step 2.3.3.1.2.2

Cancel the common factor.

$2 x - 9 = \frac{10 \cdot 9}{10 \cdot 2}$

Step 2.3.3.1.2.3

Rewrite the expression.

$2 x - 9 = \frac{9}{2}$

Step 2.4

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

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Step 2.4.1

Add $9$ to both sides of the equation.

$2 x = \frac{9}{2} + 9$

Step 2.4.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 x = \frac{9}{2} + 9 \cdot \frac{2}{2}$

Step 2.4.3

Combine $9$ and $\frac{2}{2}$ .

$2 x = \frac{9}{2} + \frac{9 \cdot 2}{2}$

Step 2.4.4

Combine the numerators over the common denominator.

$2 x = \frac{9 + 9 \cdot 2}{2}$

Step 2.4.5

Simplify the numerator.

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Step 2.4.5.1

Multiply $9$ by $2$ .

$2 x = \frac{9 + 18}{2}$

Step 2.4.5.2

Add $9$ and $18$ .

$2 x = \frac{27}{2}$

Step 2.5

Divide each term in $2 x = \frac{27}{2}$ by $2$ and simplify.

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Step 2.5.1

Divide each term in $2 x = \frac{27}{2}$ by $2$ .

$\frac{2 x}{2} = \frac{\frac{27}{2}}{2}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $2$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{\frac{27}{2}}{2}$

Step 2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{27}{2}}{2}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{27}{2} \cdot \frac{1}{2}$

Step 2.5.3.2

Multiply $\frac{27}{2} \cdot \frac{1}{2}$ .

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Step 2.5.3.2.1

Multiply $\frac{27}{2}$ by $\frac{1}{2}$ .

$x = \frac{27}{2 \cdot 2}$

Step 2.5.3.2.2

Multiply $2$ by $2$ .

$x = \frac{27}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{27}{4}$

Decimal Form:

$x = 6.75$

Mixed Number Form:

$x = 6 \frac{3}{4}$