Solve for r (5r)/2-6=19

$\frac{5 r}{2} - 6 = 19$

Step 1

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

Add $6$ to both sides of the equation.

$\frac{5 r}{2} = 19 + 6$

Add $19$ and $6$ .

$\frac{5 r}{2} = 25$

Step 2

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 r}{2} = \frac{2}{5} \cdot 25$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{5} \cdot \frac{5 r}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 r}{2} = \frac{2}{5} \cdot 25$

Rewrite the expression.

$\frac{1}{5} (5 r) = \frac{2}{5} \cdot 25$

Cancel the common factor of $5$ .

Factor $5$ out of $5 r$ .

$\frac{1}{5} (5 (r)) = \frac{2}{5} \cdot 25$

Cancel the common factor.

$\frac{1}{5} (5 r) = \frac{2}{5} \cdot 25$

Rewrite the expression.

$r = \frac{2}{5} \cdot 25$

Simplify the right side.

Simplify $\frac{2}{5} \cdot 25$ .

Cancel the common factor of $5$ .

Factor $5$ out of $25$ .

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

Cancel the common factor.

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

Rewrite the expression.

$r = 2 \cdot 5$

Multiply $2$ by $5$ .

$r = 10$