Solve for r 16-2r=3r+6r+1

$16 - 2 r = 3 r + 6 r + 1$

Since $r$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 r + 6 r + 1 = 16 - 2 r$

Add $3 r$ and $6 r$ .

$9 r + 1 = 16 - 2 r$

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

Add $2 r$ to both sides of the equation.

$9 r + 1 + 2 r = 16$

Add $9 r$ and $2 r$ .

$11 r + 1 = 16$

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

Subtract $1$ from both sides of the equation.

$11 r = 16 - 1$

Subtract $1$ from $16$ .

$11 r = 15$

Divide each term in $11 r = 15$ by $11$ and simplify.

Divide each term in $11 r = 15$ by $11$ .

$\frac{11 r}{11} = \frac{15}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 r}{11} = \frac{15}{11}$

Divide $r$ by $1$ .

$r = \frac{15}{11}$

The result can be shown in multiple forms.

Exact Form:

$r = \frac{15}{11}$

Decimal Form:

$r = 1.\overline{36}$

Mixed Number Form:

$r = 1 \frac{4}{11}$