Solve 5(2c+3)-8=3(4w-2)-7

$$5 ( 2 c + 3 ) - 8 = 3 ( 4 w - 2 ) - 7$$

Solve for c

$$c=\frac{6w}{5}-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 2c+3.

$$10c+15-8=3\left(4w-2\right)-7$$

Subtract 8 from 15 to get 7.

$$10c+7=3\left(4w-2\right)-7$$

Use the distributive property to multiply 3 by 4w-2.

$$10c+7=12w-6-7$$

Subtract 7 from -6 to get -13.

$$10c+7=12w-13$$

Subtract 7 from both sides.

$$10c=12w-13-7$$

Subtract 7 from -13 to get -20.

$$10c=12w-20$$

Divide both sides by 10.

$$\frac{10c}{10}=\frac{12w-20}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$c=\frac{12w-20}{10}$$

Divide 12w-20 by 10.

$$c=\frac{6w}{5}-2$$

Solve for w

$$w=\frac{5\left(c+2\right)}{6}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 2c+3.

$$10c+15-8=3\left(4w-2\right)-7$$

Subtract 8 from 15 to get 7.

$$10c+7=3\left(4w-2\right)-7$$

Use the distributive property to multiply 3 by 4w-2.

$$10c+7=12w-6-7$$

Subtract 7 from -6 to get -13.

$$10c+7=12w-13$$

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

$$12w-13=10c+7$$

Add 13 to both sides.

$$12w=10c+7+13$$

Add 7 and 13 to get 20.

$$12w=10c+20$$

Divide both sides by 12.

$$\frac{12w}{12}=\frac{10c+20}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$w=\frac{10c+20}{12}$$

Divide 20+10c by 12.

$$w=\frac{5c}{6}+\frac{5}{3}$$