Solve for s 1/3s+1/2=9/4+1/4s

$\frac{1}{3} s + \frac{1}{2} = \frac{9}{4} + \frac{1}{4} s$

Combine $\frac{1}{3}$ and $s$ .

$\frac{s}{3} + \frac{1}{2} = \frac{9}{4} + \frac{1}{4} s$

Combine $\frac{1}{4}$ and $s$ .

$\frac{s}{3} + \frac{1}{2} = \frac{9}{4} + \frac{s}{4}$

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

Subtract $\frac{s}{4}$ from both sides of the equation.

$\frac{s}{3} + \frac{1}{2} - \frac{s}{4} = \frac{9}{4}$

To write $\frac{s}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{s}{3} \cdot \frac{4}{4} - \frac{s}{4} + \frac{1}{2} = \frac{9}{4}$

To write $- \frac{s}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{s}{3} \cdot \frac{4}{4} - \frac{s}{4} \cdot \frac{3}{3} + \frac{1}{2} = \frac{9}{4}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{s}{3}$ by $\frac{4}{4}$ .

$\frac{s \cdot 4}{3 \cdot 4} - \frac{s}{4} \cdot \frac{3}{3} + \frac{1}{2} = \frac{9}{4}$

Multiply $3$ by $4$ .

$\frac{s \cdot 4}{12} - \frac{s}{4} \cdot \frac{3}{3} + \frac{1}{2} = \frac{9}{4}$

Multiply $\frac{s}{4}$ by $\frac{3}{3}$ .

$\frac{s \cdot 4}{12} - \frac{s \cdot 3}{4 \cdot 3} + \frac{1}{2} = \frac{9}{4}$

Multiply $4$ by $3$ .

$\frac{s \cdot 4}{12} - \frac{s \cdot 3}{12} + \frac{1}{2} = \frac{9}{4}$

Combine the numerators over the common denominator.

$\frac{s \cdot 4 - s \cdot 3}{12} + \frac{1}{2} = \frac{9}{4}$

Simplify each term.

Simplify the numerator.

Factor $s$ out of $s \cdot 4 - s \cdot 3$ .

Factor $s$ out of $s \cdot 4$ .

$\frac{s (4) - s \cdot 3}{12} + \frac{1}{2} = \frac{9}{4}$

Factor $s$ out of $- s \cdot 3$ .

$\frac{s (4) + s (- 1 \cdot 3)}{12} + \frac{1}{2} = \frac{9}{4}$

Factor $s$ out of $s (4) + s (- 1 \cdot 3)$ .

$\frac{s (4 - 1 \cdot 3)}{12} + \frac{1}{2} = \frac{9}{4}$

Multiply $- 1$ by $3$ .

$\frac{s (4 - 3)}{12} + \frac{1}{2} = \frac{9}{4}$

Subtract $3$ from $4$ .

$\frac{s \cdot 1}{12} + \frac{1}{2} = \frac{9}{4}$

Multiply $s$ by $1$ .

$\frac{s}{12} + \frac{1}{2} = \frac{9}{4}$

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

Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{s}{12} = \frac{9}{4} - \frac{1}{2}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{s}{12} = \frac{9}{4} - \frac{1}{2} \cdot \frac{2}{2}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{s}{12} = \frac{9}{4} - \frac{2}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{s}{12} = \frac{9}{4} - \frac{2}{4}$

Combine the numerators over the common denominator.

$\frac{s}{12} = \frac{9 - 2}{4}$

Subtract $2$ from $9$ .

$\frac{s}{12} = \frac{7}{4}$

Multiply both sides of the equation by $12$ .

$12 \frac{s}{12} = 12 (\frac{7}{4})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$12 \frac{s}{12} = 12 (\frac{7}{4})$

Rewrite the expression.

$s = 12 (\frac{7}{4})$

Simplify the right side.

Simplify $12 (\frac{7}{4})$ .

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$s = 4 (3) \frac{7}{4}$

Cancel the common factor.

$s = 4 \cdot 3 \frac{7}{4}$

Rewrite the expression.

$s = 3 \cdot 7$

Multiply $3$ by $7$ .

$s = 21$

Solve for s 1/3s+1/2=9/4+1/4s

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