Solve for s 2r=(5s)/2-s/4

$2 r = \frac{5 s}{2} - \frac{s}{4}$

Step 1

Rewrite the equation as $\frac{5 s}{2} - \frac{s}{4} = 2 r$ .

$\frac{5 s}{2} - \frac{s}{4} = 2 r$

Step 2

Simplify $\frac{5 s}{2} - \frac{s}{4}$ .

To write $\frac{5 s}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 s}{2} \cdot \frac{2}{2} - \frac{s}{4} = 2 r$

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

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

$\frac{5 s \cdot 2}{2 \cdot 2} - \frac{s}{4} = 2 r$

Multiply $2$ by $2$ .

$\frac{5 s \cdot 2}{4} - \frac{s}{4} = 2 r$

Combine the numerators over the common denominator.

$\frac{5 s \cdot 2 - s}{4} = 2 r$

Simplify the numerator.

Factor $s$ out of $5 s \cdot 2 - s$ .

Factor $s$ out of $5 s \cdot 2$ .

$\frac{s (5 \cdot 2) - s}{4} = 2 r$

Factor $s$ out of $- s$ .

$\frac{s (5 \cdot 2) + s \cdot - 1}{4} = 2 r$

Factor $s$ out of $s (5 \cdot 2) + s \cdot - 1$ .

$\frac{s (5 \cdot 2 - 1)}{4} = 2 r$

Multiply $5$ by $2$ .

$\frac{s (10 - 1)}{4} = 2 r$

Subtract $1$ from $10$ .

$\frac{s \cdot 9}{4} = 2 r$

Move $9$ to the left of $s$ .

$\frac{9 s}{4} = 2 r$

Step 3

Multiply both sides of the equation by $\frac{4}{9}$ .

$\frac{4}{9} \cdot \frac{9 s}{4} = \frac{4}{9} (2 r)$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{9} \cdot \frac{9 s}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{9} \cdot \frac{9 s}{4} = \frac{4}{9} (2 r)$

Rewrite the expression.

$\frac{1}{9} (9 s) = \frac{4}{9} (2 r)$

Cancel the common factor of $9$ .

Factor $9$ out of $9 s$ .

$\frac{1}{9} (9 (s)) = \frac{4}{9} (2 r)$

Cancel the common factor.

$\frac{1}{9} (9 s) = \frac{4}{9} (2 r)$

Rewrite the expression.

$s = \frac{4}{9} (2 r)$

Simplify the right side.

Multiply $\frac{4}{9} (2 r)$ .

Combine $2$ and $\frac{4}{9}$ .

$s = \frac{2 \cdot 4}{9} r$

Multiply $2$ by $4$ .

$s = \frac{8}{9} r$

Combine $\frac{8}{9}$ and $r$ .

$s = \frac{8 r}{9}$

Solve for s 2r=(5s)/2-s/4

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