Solve for x -5/6x-7/30x+1/5x=-52

$- \frac{5}{6} x - \frac{7}{30} x + \frac{1}{5} x = - 52$

Step 1

Simplify $- \frac{5}{6} x - \frac{7}{30} x + \frac{1}{5} x$ .

Simplify each term.

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

$- \frac{x \cdot 5}{6} - \frac{7}{30} x + \frac{1}{5} x = - 52$

Move $5$ to the left of $x$ .

$- \frac{5 \cdot x}{6} - \frac{7}{30} x + \frac{1}{5} x = - 52$

Combine $x$ and $\frac{7}{30}$ .

$- \frac{5 x}{6} - \frac{x \cdot 7}{30} + \frac{1}{5} x = - 52$

Move $7$ to the left of $x$ .

$- \frac{5 x}{6} - \frac{7 \cdot x}{30} + \frac{1}{5} x = - 52$

Combine $\frac{1}{5}$ and $x$ .

$- \frac{5 x}{6} - \frac{7 x}{30} + \frac{x}{5} = - 52$

Find the common denominator.

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

$- (\frac{5 x}{6} \cdot \frac{5}{5}) - \frac{7 x}{30} + \frac{x}{5} = - 52$

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

$- \frac{5 x \cdot 5}{6 \cdot 5} - \frac{7 x}{30} + \frac{x}{5} = - 52$

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

$- \frac{5 x \cdot 5}{6 \cdot 5} - \frac{7 x}{30} + \frac{x}{5} \cdot \frac{6}{6} = - 52$

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

$- \frac{5 x \cdot 5}{6 \cdot 5} - \frac{7 x}{30} + \frac{x \cdot 6}{5 \cdot 6} = - 52$

Reorder the factors of $6 \cdot 5$ .

$- \frac{5 x \cdot 5}{5 \cdot 6} - \frac{7 x}{30} + \frac{x \cdot 6}{5 \cdot 6} = - 52$

Multiply $5$ by $6$ .

$- \frac{5 x \cdot 5}{30} - \frac{7 x}{30} + \frac{x \cdot 6}{5 \cdot 6} = - 52$

Multiply $5$ by $6$ .

$- \frac{5 x \cdot 5}{30} - \frac{7 x}{30} + \frac{x \cdot 6}{30} = - 52$

Combine the numerators over the common denominator.

$\frac{- 5 x \cdot 5 - 7 x + x \cdot 6}{30} = - 52$

Simplify each term.

Multiply $5$ by $- 5$ .

$\frac{- 25 x - 7 x + x \cdot 6}{30} = - 52$

Move $6$ to the left of $x$ .

$\frac{- 25 x - 7 x + 6 x}{30} = - 52$

Simplify terms.

Subtract $7 x$ from $- 25 x$ .

$\frac{- 32 x + 6 x}{30} = - 52$

Add $- 32 x$ and $6 x$ .

$\frac{- 26 x}{30} = - 52$

Cancel the common factor of $- 26$ and $30$ .

Factor $2$ out of $- 26 x$ .

$\frac{2 (- 13 x)}{30} = - 52$

Cancel the common factors.

Factor $2$ out of $30$ .

$\frac{2 (- 13 x)}{2 (15)} = - 52$

Cancel the common factor.

$\frac{2 (- 13 x)}{2 \cdot 15} = - 52$

Rewrite the expression.

$\frac{- 13 x}{15} = - 52$

Move the negative in front of the fraction.

$- \frac{13 x}{15} = - 52$

Step 2

Multiply both sides of the equation by $- \frac{15}{13}$ .

$- \frac{15}{13} (- \frac{13 x}{15}) = - \frac{15}{13} \cdot - 52$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{15}{13} (- \frac{13 x}{15})$ .

Cancel the common factor of $15$ .

Move the leading negative in $- \frac{15}{13}$ into the numerator.

$\frac{- 15}{13} (- \frac{13 x}{15}) = - \frac{15}{13} \cdot - 52$

Move the leading negative in $- \frac{13 x}{15}$ into the numerator.

$\frac{- 15}{13} \cdot \frac{- 13 x}{15} = - \frac{15}{13} \cdot - 52$

Factor $15$ out of $- 15$ .

$\frac{15 (- 1)}{13} \cdot \frac{- 13 x}{15} = - \frac{15}{13} \cdot - 52$

Cancel the common factor.

$\frac{15 \cdot - 1}{13} \cdot \frac{- 13 x}{15} = - \frac{15}{13} \cdot - 52$

Rewrite the expression.

$\frac{- 1}{13} (- 13 x) = - \frac{15}{13} \cdot - 52$

Cancel the common factor of $13$ .

Factor $13$ out of $- 13 x$ .

$\frac{- 1}{13} (13 (- x)) = - \frac{15}{13} \cdot - 52$

Cancel the common factor.

$\frac{- 1}{13} (13 (- x)) = - \frac{15}{13} \cdot - 52$

Rewrite the expression.

$- - x = - \frac{15}{13} \cdot - 52$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{15}{13} \cdot - 52$

Multiply $x$ by $1$ .

$x = - \frac{15}{13} \cdot - 52$

Simplify the right side.

Simplify $- \frac{15}{13} \cdot - 52$ .

Cancel the common factor of $13$ .

Move the leading negative in $- \frac{15}{13}$ into the numerator.

$x = \frac{- 15}{13} \cdot - 52$

Factor $13$ out of $- 52$ .

$x = \frac{- 15}{13} \cdot (13 (- 4))$

Cancel the common factor.

$x = \frac{- 15}{13} \cdot (13 \cdot - 4)$

Rewrite the expression.

$x = - 15 \cdot - 4$

Multiply $- 15$ by $- 4$ .

$x = 60$

Solve for x -5/6x-7/30x+1/5x=-52

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