Solve 1/3(r+2s)-1-2s/5=-4

$$\frac { 1 } { 3 } ( r + 2 s ) - \frac { 1 - 2 s } { 5 } = - 4$$

Solve for r

$$r=\frac{-16s-57}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(r+2s\right)-3\left(1-2s\right)=-60$$

Use the distributive property to multiply 5 by r+2s.

$$5r+10s-3\left(1-2s\right)=-60$$

Use the distributive property to multiply -3 by 1-2s.

$$5r+10s-3+6s=-60$$

Combine 10s and 6s to get 16s.

$$5r+16s-3=-60$$

Subtract 16s from both sides.

$$5r-3=-60-16s$$

Add 3 to both sides.

$$5r=-60-16s+3$$

Add -60 and 3 to get -57.

$$5r=-57-16s$$

The equation is in standard form.

$$5r=-16s-57$$

Divide both sides by 5.

$$\frac{5r}{5}=\frac{-16s-57}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$r=\frac{-16s-57}{5}$$

Solve for s

$$s=\frac{-5r-57}{16}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(r+2s\right)-3\left(1-2s\right)=-60$$

Use the distributive property to multiply 5 by r+2s.

$$5r+10s-3\left(1-2s\right)=-60$$

Use the distributive property to multiply -3 by 1-2s.

$$5r+10s-3+6s=-60$$

Combine 10s and 6s to get 16s.

$$5r+16s-3=-60$$

Subtract 5r from both sides.

$$16s-3=-60-5r$$

Add 3 to both sides.

$$16s=-60-5r+3$$

Add -60 and 3 to get -57.

$$16s=-57-5r$$

The equation is in standard form.

$$16s=-5r-57$$

Divide both sides by 16.

$$\frac{16s}{16}=\frac{-5r-57}{16}$$

Dividing by 16 undoes the multiplication by 16.

$$s=\frac{-5r-57}{16}$$