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

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

Solve for w

$$w=\frac{2}{7}\approx 0.285714286$$

Steps for Solving Linear Equation

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

$$2\left(1-3w-6+2\left(w+3\right)\right)=5w$$

Subtract 6 from 1 to get -5.

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

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

$$2\left(-5-3w+2w+6\right)=5w$$

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

$$2\left(-5-w+6\right)=5w$$

Add -5 and 6 to get 1.

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

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

$$2-2w=5w$$

Subtract 5w from both sides.

$$2-2w-5w=0$$

Combine -2w and -5w to get -7w.

$$2-7w=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-7w=-2$$

Divide both sides by -7.

$$w=\frac{-2}{-7}$$

Fraction \frac{-2}{-7} can be simplified to \frac{2}{7} by removing the negative sign from both the numerator and the denominator.

$$w=\frac{2}{7}$$