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

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

Solve for w

$$w = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

Steps for Solving Linear Equation

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

$$1+8w-12=-3\left(3w-1\right)+7w$$

Subtract 12 from 1 to get -11.

$$-11+8w=-3\left(3w-1\right)+7w$$

Use the distributive property to multiply -3 by 3w-1.

$$-11+8w=-9w+3+7w$$

Combine -9w and 7w to get -2w.

$$-11+8w=-2w+3$$

Add 2w to both sides.

$$-11+8w+2w=3$$

Combine 8w and 2w to get 10w.

$$-11+10w=3$$

Add 11 to both sides.

$$10w=3+11$$

Add 3 and 11 to get 14.

$$10w=14$$

Divide both sides by 10.

$$w=\frac{14}{10}$$

Reduce the fraction \frac{14}{10} to lowest terms by extracting and canceling out 2.

$$w=\frac{7}{5}$$