Solve for x 3/10x+7=1/6-x

$\frac{3}{10} x + 7 = \frac{1}{6} - x$

Combine $\frac{3}{10}$ and $x$ .

$\frac{3 x}{10} + 7 = \frac{1}{6} - x$

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$\frac{3 x}{10} + 7 + x = \frac{1}{6}$

To write $x$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{3 x}{10} + x \cdot \frac{10}{10} + 7 = \frac{1}{6}$

Combine $x$ and $\frac{10}{10}$ .

$\frac{3 x}{10} + \frac{x \cdot 10}{10} + 7 = \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{3 x + x \cdot 10}{10} + 7 = \frac{1}{6}$

Add $3 x$ and $x \cdot 10$ .

Reorder $x$ and $10$ .

$\frac{3 x + 10 \cdot x}{10} + 7 = \frac{1}{6}$

Add $3 x$ and $10 \cdot x$ .

$\frac{13 x}{10} + 7 = \frac{1}{6}$

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

Subtract $7$ from both sides of the equation.

$\frac{13 x}{10} = \frac{1}{6} - 7$

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{13 x}{10} = \frac{1}{6} - 7 \cdot \frac{6}{6}$

Combine $- 7$ and $\frac{6}{6}$ .

$\frac{13 x}{10} = \frac{1}{6} + \frac{- 7 \cdot 6}{6}$

Combine the numerators over the common denominator.

$\frac{13 x}{10} = \frac{1 - 7 \cdot 6}{6}$

Simplify the numerator.

Multiply $- 7$ by $6$ .

$\frac{13 x}{10} = \frac{1 - 42}{6}$

Subtract $42$ from $1$ .

$\frac{13 x}{10} = \frac{- 41}{6}$

Move the negative in front of the fraction.

$\frac{13 x}{10} = - \frac{41}{6}$

Multiply both sides of the equation by $\frac{10}{13}$ .

$\frac{10}{13} \cdot \frac{13 x}{10} = \frac{10}{13} (- \frac{41}{6})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{10}{13} \cdot \frac{13 x}{10}$ .

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10}{13} \cdot \frac{13 x}{10} = \frac{10}{13} (- \frac{41}{6})$

Rewrite the expression.

$\frac{1}{13} (13 x) = \frac{10}{13} (- \frac{41}{6})$

Cancel the common factor of $13$ .

Factor $13$ out of $13 x$ .

$\frac{1}{13} (13 (x)) = \frac{10}{13} (- \frac{41}{6})$

Cancel the common factor.

$\frac{1}{13} (13 x) = \frac{10}{13} (- \frac{41}{6})$

Rewrite the expression.

$x = \frac{10}{13} (- \frac{41}{6})$

Simplify the right side.

Simplify $\frac{10}{13} (- \frac{41}{6})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{41}{6}$ into the numerator.

$x = \frac{10}{13} \cdot \frac{- 41}{6}$

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{13} \cdot \frac{- 41}{6}$

Factor $2$ out of $6$ .

$x = \frac{2 \cdot 5}{13} \cdot \frac{- 41}{2 \cdot 3}$

Cancel the common factor.

$x = \frac{2 \cdot 5}{13} \cdot \frac{- 41}{2 \cdot 3}$

Rewrite the expression.

$x = \frac{5}{13} \cdot \frac{- 41}{3}$

Multiply $\frac{5}{13}$ by $\frac{- 41}{3}$ .

$x = \frac{5 \cdot - 41}{13 \cdot 3}$

Simplify the expression.

Multiply $5$ by $- 41$ .

$x = \frac{- 205}{13 \cdot 3}$

Multiply $13$ by $3$ .

$x = \frac{- 205}{39}$

Move the negative in front of the fraction.

$x = - \frac{205}{39}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{205}{39}$

Decimal Form:

$x = - 5.\overline{256410}$

Mixed Number Form:

$x = - 5 \frac{10}{39}$

Solve for x 3/10x+7=1/6-x

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