Solve for x x/6=3 1/2

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

Step 1

Simplify the right side.

Convert $3 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $3$ and $\frac{1}{2}$ .

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{x}{6} = \frac{6 + 1}{2}$

Add $6$ and $1$ .

$\frac{x}{6} = \frac{7}{2}$

Step 2

Multiply both sides of the equation by $6$ .

$6 \frac{x}{6} = 6 (\frac{7}{2})$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$6 \frac{x}{6} = 6 (\frac{7}{2})$

Rewrite the expression.

$x = 6 (\frac{7}{2})$

Simplify the right side.

Simplify $6 (\frac{7}{2})$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$x = 2 (3) \frac{7}{2}$

Cancel the common factor.

$x = 2 \cdot 3 \frac{7}{2}$

Rewrite the expression.

$x = 3 \cdot 7$

Multiply $3$ by $7$ .

$x = 21$