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

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

Solve for w

$$w=-\frac{7}{11}\approx -0.636363636$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5 by w+3.

$$2-5w-15+2\left(w+1\right)=2\left(5w+1-\left(w+3\right)\right)$$

Subtract 15 from 2 to get -13.

$$-13-5w+2\left(w+1\right)=2\left(5w+1-\left(w+3\right)\right)$$

Use the distributive property to multiply 2 by w+1.

$$-13-5w+2w+2=2\left(5w+1-\left(w+3\right)\right)$$

Combine -5w and 2w to get -3w.

$$-13-3w+2=2\left(5w+1-\left(w+3\right)\right)$$

Add -13 and 2 to get -11.

$$-11-3w=2\left(5w+1-\left(w+3\right)\right)$$

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

$$-11-3w=2\left(5w+1-w-3\right)$$

Combine 5w and -w to get 4w.

$$-11-3w=2\left(4w+1-3\right)$$

Subtract 3 from 1 to get -2.

$$-11-3w=2\left(4w-2\right)$$

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

$$-11-3w=8w-4$$

Subtract 8w from both sides.

$$-11-3w-8w=-4$$

Combine -3w and -8w to get -11w.

$$-11-11w=-4$$

Add 11 to both sides.

$$-11w=-4+11$$

Add -4 and 11 to get 7.

$$-11w=7$$

Divide both sides by -11.

$$w=\frac{7}{-11}$$

Fraction \frac{7}{-11} can be rewritten as -\frac{7}{11} by extracting the negative sign.

$$w=-\frac{7}{11}$$