Solve w-2[w+5(1-2w)+4w]-(w+3)=-w+3(w+2)+7w

$$w - 2 [ w + 5 ( 1 - 2 w ) + 4 w ] - ( w + 3 ) = - w + 3 ( w + 2 ) + 7 w$$

Solve for w

$$w=19$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 1-2w.

$$w-2\left(w+5-10w+4w\right)-\left(w+3\right)=-w+3\left(w+2\right)+7w$$

Combine w and -10w to get -9w.

$$w-2\left(-9w+5+4w\right)-\left(w+3\right)=-w+3\left(w+2\right)+7w$$

Combine -9w and 4w to get -5w.

$$w-2\left(-5w+5\right)-\left(w+3\right)=-w+3\left(w+2\right)+7w$$

Use the distributive property to multiply -2 by -5w+5.

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

Combine w and 10w to get 11w.

$$11w-10-\left(w+3\right)=-w+3\left(w+2\right)+7w$$

To find the opposite of w+3, find the opposite of each term.

$$11w-10-w-3=-w+3\left(w+2\right)+7w$$

Combine 11w and -w to get 10w.

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

Subtract 3 from -10 to get -13.

$$10w-13=-w+3\left(w+2\right)+7w$$

Use the distributive property to multiply 3 by w+2.

$$10w-13=-w+3w+6+7w$$

Combine 3w and 7w to get 10w.

$$10w-13=-w+10w+6$$

Add w to both sides.

$$10w-13+w=10w+6$$

Combine 10w and w to get 11w.

$$11w-13=10w+6$$

Subtract 10w from both sides.

$$11w-13-10w=6$$

Combine 11w and -10w to get w.

$$w-13=6$$

Add 13 to both sides.

$$w=6+13$$

Add 6 and 13 to get 19.

$$w=19$$