Solve 3(r+2s)=2t-4

$$3(r+2s)=2t-4$$

Solve for r

$$r=\frac{2\left(-3s+t-2\right)}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by r+2s.

$$3r+6s=2t-4$$

Subtract 6s from both sides.

$$3r=2t-4-6s$$

The equation is in standard form.

$$3r=-6s+2t-4$$

Divide both sides by 3.

$$\frac{3r}{3}=\frac{-6s+2t-4}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$r=\frac{-6s+2t-4}{3}$$

Divide -4+2t-6s by 3.

$$r=\frac{2t}{3}-2s-\frac{4}{3}$$

Solve for s

$$s=\frac{t}{3}-\frac{r}{2}-\frac{2}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by r+2s.

$$3r+6s=2t-4$$

Subtract 3r from both sides.

$$6s=2t-4-3r$$

The equation is in standard form.

$$6s=-3r+2t-4$$

Divide both sides by 6.

$$\frac{6s}{6}=\frac{-3r+2t-4}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$s=\frac{-3r+2t-4}{6}$$

Divide 2t-4-3r by 6.

$$s=\frac{t}{3}-\frac{r}{2}-\frac{2}{3}$$

Solve for t

$$t=\frac{3r}{2}+3s+2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by r+2s.

$$3r+6s=2t-4$$

Swap sides so that all variable terms are on the left hand side.

$$2t-4=3r+6s$$

Add 4 to both sides.

$$2t=3r+6s+4$$

Divide both sides by 2.

$$\frac{2t}{2}=\frac{3r+6s+4}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$t=\frac{3r+6s+4}{2}$$

Divide 3r+6s+4 by 2.

$$t=\frac{3r}{2}+3s+2$$