Precalculus Examples

$\frac{3}{5 - 2 x} = \frac{7}{2}$

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.

$3 \cdot 2 = (5 - 2 x) \cdot 7$

Step 2

Solve the equation for $x$ .

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Step 2.1

Rewrite the equation as $(5 - 2 x) \cdot 7 = 3 \cdot 2$ .

$(5 - 2 x) \cdot 7 = 3 \cdot 2$

Step 2.2

Multiply $3$ by $2$ .

$(5 - 2 x) \cdot 7 = 6$

Step 2.3

Divide each term in $(5 - 2 x) \cdot 7 = 6$ by $7$ and simplify.

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Step 2.3.1

Divide each term in $(5 - 2 x) \cdot 7 = 6$ by $7$ .

$\frac{(5 - 2 x) \cdot 7}{7} = \frac{6}{7}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $7$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{(5 - 2 x) \cdot 7}{7} = \frac{6}{7}$

Step 2.3.2.1.2

Divide $5 - 2 x$ by $1$ .

$5 - 2 x = \frac{6}{7}$

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 $5$ from both sides of the equation.

$- 2 x = \frac{6}{7} - 5$

Step 2.4.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- 2 x = \frac{6}{7} - 5 \cdot \frac{7}{7}$

Step 2.4.3

Combine $- 5$ and $\frac{7}{7}$ .

$- 2 x = \frac{6}{7} + \frac{- 5 \cdot 7}{7}$

Step 2.4.4

Combine the numerators over the common denominator.

$- 2 x = \frac{6 - 5 \cdot 7}{7}$

Step 2.4.5

Simplify the numerator.

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Step 2.4.5.1

Multiply $- 5$ by $7$ .

$- 2 x = \frac{6 - 35}{7}$

Step 2.4.5.2

Subtract $35$ from $6$ .

$- 2 x = \frac{- 29}{7}$

Step 2.4.6

Move the negative in front of the fraction.

$- 2 x = - \frac{29}{7}$

Step 2.5

Divide each term in $- 2 x = - \frac{29}{7}$ by $- 2$ and simplify.

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Step 2.5.1

Divide each term in $- 2 x = - \frac{29}{7}$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- \frac{29}{7}}{- 2}$

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.

$\frac{- 2 x}{- 2} = \frac{- \frac{29}{7}}{- 2}$

Step 2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{29}{7}}{- 2}$

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.

$x = - \frac{29}{7} \cdot \frac{1}{- 2}$

Step 2.5.3.2

Move the negative in front of the fraction.

$x = - \frac{29}{7} (- \frac{1}{2})$

Step 2.5.3.3

Multiply $- \frac{29}{7} (- \frac{1}{2})$ .

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Step 2.5.3.3.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{29}{7}) \frac{1}{2}$

Step 2.5.3.3.2

Multiply $\frac{29}{7}$ by $1$ .

$x = \frac{29}{7} \cdot \frac{1}{2}$

Step 2.5.3.3.3

Multiply $\frac{29}{7}$ by $\frac{1}{2}$ .

$x = \frac{29}{7 \cdot 2}$

Step 2.5.3.3.4

Multiply $7$ by $2$ .

$x = \frac{29}{14}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{29}{14}$

Decimal Form:

$x = 2.07142857 \dots$

Mixed Number Form:

$x = 2 \frac{1}{14}$