Solve for x 3/5(x+1/6)=-23/10

$\frac{3}{5} (x + \frac{1}{6}) = - \frac{23}{10}$

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} (\frac{3}{5} \cdot (x + \frac{1}{6})) = \frac{5}{3} (- \frac{23}{10})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{3} (\frac{3}{5} \cdot (x + \frac{1}{6}))$ .

Apply the distributive property.

$\frac{5}{3} (\frac{3}{5} x + \frac{3}{5} \cdot \frac{1}{6}) = \frac{5}{3} (- \frac{23}{10})$

Combine $\frac{3}{5}$ and $x$ .

$\frac{5}{3} (\frac{3 x}{5} + \frac{3}{5} \cdot \frac{1}{6}) = \frac{5}{3} (- \frac{23}{10})$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{5}{3} (\frac{3 x}{5} + \frac{3}{5} \cdot \frac{1}{3 (2)}) = \frac{5}{3} (- \frac{23}{10})$

Cancel the common factor.

$\frac{5}{3} (\frac{3 x}{5} + \frac{3}{5} \cdot \frac{1}{3 \cdot 2}) = \frac{5}{3} (- \frac{23}{10})$

Rewrite the expression.

$\frac{5}{3} (\frac{3 x}{5} + \frac{1}{5} \cdot \frac{1}{2}) = \frac{5}{3} (- \frac{23}{10})$

Multiply $\frac{1}{5}$ by $\frac{1}{2}$ .

$\frac{5}{3} (\frac{3 x}{5} + \frac{1}{5 \cdot 2}) = \frac{5}{3} (- \frac{23}{10})$

Multiply $5$ by $2$ .

$\frac{5}{3} (\frac{3 x}{5} + \frac{1}{10}) = \frac{5}{3} (- \frac{23}{10})$

Apply the distributive property.

$\frac{5}{3} \cdot \frac{3 x}{5} + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 x}{5} + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Rewrite the expression.

$\frac{1}{3} (3 x) + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Cancel the common factor.

$\frac{1}{3} (3 x) + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Rewrite the expression.

$x + \frac{5}{3} \cdot \frac{1}{10} = \frac{5}{3} (- \frac{23}{10})$

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$x + \frac{5}{3} \cdot \frac{1}{5 (2)} = \frac{5}{3} (- \frac{23}{10})$

Cancel the common factor.

$x + \frac{5}{3} \cdot \frac{1}{5 \cdot 2} = \frac{5}{3} (- \frac{23}{10})$

Rewrite the expression.

$x + \frac{1}{3} \cdot \frac{1}{2} = \frac{5}{3} (- \frac{23}{10})$

Multiply $\frac{1}{3}$ by $\frac{1}{2}$ .

$x + \frac{1}{3 \cdot 2} = \frac{5}{3} (- \frac{23}{10})$

Multiply $3$ by $2$ .

$x + \frac{1}{6} = \frac{5}{3} (- \frac{23}{10})$

Simplify the right side.

Simplify $\frac{5}{3} (- \frac{23}{10})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{23}{10}$ into the numerator.

$x + \frac{1}{6} = \frac{5}{3} \cdot \frac{- 23}{10}$

Factor $5$ out of $10$ .

$x + \frac{1}{6} = \frac{5}{3} \cdot \frac{- 23}{5 (2)}$

Cancel the common factor.

$x + \frac{1}{6} = \frac{5}{3} \cdot \frac{- 23}{5 \cdot 2}$

Rewrite the expression.

$x + \frac{1}{6} = \frac{1}{3} \cdot \frac{- 23}{2}$

Multiply $\frac{1}{3}$ by $\frac{- 23}{2}$ .

$x + \frac{1}{6} = \frac{- 23}{3 \cdot 2}$

Simplify the expression.

Multiply $3$ by $2$ .

$x + \frac{1}{6} = \frac{- 23}{6}$

Move the negative in front of the fraction.

$x + \frac{1}{6} = - \frac{23}{6}$

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

Subtract $\frac{1}{6}$ from both sides of the equation.

$x = - \frac{23}{6} - \frac{1}{6}$

Combine the numerators over the common denominator.

$x = \frac{- 23 - 1}{6}$

Subtract $1$ from $- 23$ .

$x = \frac{- 24}{6}$

Divide $- 24$ by $6$ .

$x = - 4$

Solve for x 3/5(x+1/6)=-23/10

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