Solve for x 5/6(x-5/2)=65/12

$\frac{5}{6} (x - \frac{5}{2}) = \frac{65}{12}$

Step 1

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} (\frac{5}{6} \cdot (x - \frac{5}{2})) = \frac{6}{5} \cdot \frac{65}{12}$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{5} (\frac{5}{6} \cdot (x - \frac{5}{2}))$ .

Apply the distributive property.

$\frac{6}{5} (\frac{5}{6} x + \frac{5}{6} (- \frac{5}{2})) = \frac{6}{5} \cdot \frac{65}{12}$

Combine $\frac{5}{6}$ and $x$ .

$\frac{6}{5} (\frac{5 x}{6} + \frac{5}{6} (- \frac{5}{2})) = \frac{6}{5} \cdot \frac{65}{12}$

Multiply $\frac{5}{6} (- \frac{5}{2})$ .

Multiply $\frac{5}{6}$ by $\frac{5}{2}$ .

$\frac{6}{5} (\frac{5 x}{6} - \frac{5 \cdot 5}{6 \cdot 2}) = \frac{6}{5} \cdot \frac{65}{12}$

Multiply $5$ by $5$ .

$\frac{6}{5} (\frac{5 x}{6} - \frac{25}{6 \cdot 2}) = \frac{6}{5} \cdot \frac{65}{12}$

Multiply $6$ by $2$ .

$\frac{6}{5} (\frac{5 x}{6} - \frac{25}{12}) = \frac{6}{5} \cdot \frac{65}{12}$

Apply the distributive property.

$\frac{6}{5} \cdot \frac{5 x}{6} + \frac{6}{5} (- \frac{25}{12}) = \frac{6}{5} \cdot \frac{65}{12}$

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 x}{6} + \frac{6}{5} (- \frac{25}{12}) = \frac{6}{5} \cdot \frac{65}{12}$

Rewrite the expression.

$\frac{1}{5} (5 x) + \frac{6}{5} (- \frac{25}{12}) = \frac{6}{5} \cdot \frac{65}{12}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) + \frac{6}{5} (- \frac{25}{12}) = \frac{6}{5} \cdot \frac{65}{12}$

Cancel the common factor.

$\frac{1}{5} (5 x) + \frac{6}{5} (- \frac{25}{12}) = \frac{6}{5} \cdot \frac{65}{12}$

Rewrite the expression.

$x + \frac{6}{5} (- \frac{25}{12}) = \frac{6}{5} \cdot \frac{65}{12}$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{25}{12}$ into the numerator.

$x + \frac{6}{5} \cdot \frac{- 25}{12} = \frac{6}{5} \cdot \frac{65}{12}$

Factor $6$ out of $12$ .

$x + \frac{6}{5} \cdot \frac{- 25}{6 (2)} = \frac{6}{5} \cdot \frac{65}{12}$

Cancel the common factor.

$x + \frac{6}{5} \cdot \frac{- 25}{6 \cdot 2} = \frac{6}{5} \cdot \frac{65}{12}$

Rewrite the expression.

$x + \frac{1}{5} \cdot \frac{- 25}{2} = \frac{6}{5} \cdot \frac{65}{12}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 25$ .

$x + \frac{1}{5} \cdot \frac{5 (- 5)}{2} = \frac{6}{5} \cdot \frac{65}{12}$

Cancel the common factor.

$x + \frac{1}{5} \cdot \frac{5 \cdot - 5}{2} = \frac{6}{5} \cdot \frac{65}{12}$

Rewrite the expression.

$x + \frac{- 5}{2} = \frac{6}{5} \cdot \frac{65}{12}$

Move the negative in front of the fraction.

$x - \frac{5}{2} = \frac{6}{5} \cdot \frac{65}{12}$

Simplify the right side.

Simplify $\frac{6}{5} \cdot \frac{65}{12}$ .

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$x - \frac{5}{2} = \frac{6}{5} \cdot \frac{65}{6 (2)}$

Cancel the common factor.

$x - \frac{5}{2} = \frac{6}{5} \cdot \frac{65}{6 \cdot 2}$

Rewrite the expression.

$x - \frac{5}{2} = \frac{1}{5} \cdot \frac{65}{2}$

Cancel the common factor of $5$ .

Factor $5$ out of $65$ .

$x - \frac{5}{2} = \frac{1}{5} \cdot \frac{5 (13)}{2}$

Cancel the common factor.

$x - \frac{5}{2} = \frac{1}{5} \cdot \frac{5 \cdot 13}{2}$

Rewrite the expression.

$x - \frac{5}{2} = \frac{13}{2}$

Step 3

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

Add $\frac{5}{2}$ to both sides of the equation.

$x = \frac{13}{2} + \frac{5}{2}$

Combine the numerators over the common denominator.

$x = \frac{13 + 5}{2}$

Add $13$ and $5$ .

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

Divide $18$ by $2$ .

$x = 9$

Solve for x 5/6(x-5/2)=65/12

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