Solve 27-[3y-(2y+1)]=4y-[27+(3y-2)-(5-12)]

$$27 - [ 3 y - ( 2 y + 1 ) ] = 4 y - [ 27 + ( 3 y - 2 ) - ( 5 - 12 ) ]$$

Solve for y

$$y=30$$

Steps for Solving Linear Equation

To find the opposite of 2y+1, find the opposite of each term.

$$27-\left(3y-2y-1\right)=4y-\left(27+3y-2-\left(5-12\right)\right)$$

Combine 3y and -2y to get y.

$$27-\left(y-1\right)=4y-\left(27+3y-2-\left(5-12\right)\right)$$

To find the opposite of y-1, find the opposite of each term.

$$27-y-\left(-1\right)=4y-\left(27+3y-2-\left(5-12\right)\right)$$

The opposite of -1 is 1.

$$27-y+1=4y-\left(27+3y-2-\left(5-12\right)\right)$$

Add 27 and 1 to get 28.

$$28-y=4y-\left(27+3y-2-\left(5-12\right)\right)$$

Subtract 2 from 27 to get 25.

$$28-y=4y-\left(25+3y-\left(5-12\right)\right)$$

Subtract 12 from 5 to get -7.

$$28-y=4y-\left(25+3y-\left(-7\right)\right)$$

The opposite of -7 is 7.

$$28-y=4y-\left(25+3y+7\right)$$

To find the opposite of 25+3y+7, find the opposite of each term.

$$28-y=4y-25-3y-7$$

Combine 4y and -3y to get y.

$$28-y=y-25-7$$

Subtract 7 from -25 to get -32.

$$28-y=y-32$$

Subtract y from both sides.

$$28-y-y=-32$$

Combine -y and -y to get -2y.

$$28-2y=-32$$

Subtract 28 from both sides.

$$-2y=-32-28$$

Subtract 28 from -32 to get -60.

$$-2y=-60$$

Divide both sides by -2.

$$y=\frac{-60}{-2}$$

Divide -60 by -2 to get 30.

$$y=30$$