Solve for x 3-1/6x=3/2

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

Step 1

Combine $x$ and $\frac{1}{6}$ .

$3 - \frac{x}{6} = \frac{3}{2}$

Step 2

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

Subtract $3$ from both sides of the equation.

$- \frac{x}{6} = \frac{3}{2} - 3$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $- 3$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 3$ by $2$ .

$- \frac{x}{6} = \frac{3 - 6}{2}$

Subtract $6$ from $3$ .

$- \frac{x}{6} = \frac{- 3}{2}$

Move the negative in front of the fraction.

$- \frac{x}{6} = - \frac{3}{2}$

Step 3

Multiply both sides of the equation by $- 6$ .

$- 6 (- \frac{x}{6}) = - 6 (- \frac{3}{2})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $6$ .

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

$- 6 \frac{- x}{6} = - 6 (- \frac{3}{2})$

Factor $6$ out of $- 6$ .

$6 (- 1) \frac{- x}{6} = - 6 (- \frac{3}{2})$

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 6 (- \frac{3}{2})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 6 (- \frac{3}{2})$

Multiply $x$ by $1$ .

$x = - 6 (- \frac{3}{2})$

Simplify the right side.

Simplify $- 6 (- \frac{3}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$x = - 6 (\frac{- 3}{2})$

Factor $2$ out of $- 6$ .

$x = 2 (- 3) \frac{- 3}{2}$

Cancel the common factor.

$x = 2 \cdot - 3 \frac{- 3}{2}$

Rewrite the expression.

$x = - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$x = 9$

Solve for x 3-1/6x=3/2

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