5 (x-1) + 6 (x+2) - 7 (x-3) = 8 (x+1)

Distribute the 5,6,-7.

Then collect the like terms calculate the sum or difference.

Move constant to right side.

Movie variable to left side and change it's sign.

Collect like terms.

Did use both sides by - 4.

Answer=x=7

Are you simplifying the equation or solving for x?

Finding x:

You first expand the three terms in parenthesis, you do this by taking

5 (x - 1) and multiplying 5 by x and - 1 which gives 5x - 5, you repeat this for 6 (x + 2), - 7 (x - 3) and 8 (x + 1) which gives 6x + 12, - 7x + 21 and 8x + 8

Collectively we have the equation 5x - 5 + 6x + 12 - 7x + 21 = 8x + 8

Next we group the like terms

5x + 6x - 7x

5 + 6 = 11 and 11 - 7 = 4, thus we have 4x and - 5 + 12 + 21 = 28

Now the equation has been simplified to 4x + 28 = 8x + 8

Then we subtract each side by 28 which is 4x = 8x - 20

Then 8x is subtracted from each side, giving - 4x = - 20

Lastly both sides are divided by - 4 to isolate x which gives x = 5

Fully simplified:

To have the equation fully simplified you just stop at 4x + 28 = 8x + 8 if it is an answer choice, if it is not factor the equation.

I will be using GFC (Greatest Common Factor) to factor.

We start factoring at turning 28 into 4 * 7

4x + 28 = 4x + 4 * 7

4 being the common factor gets factored out, leaving 4 (x+7)

Repeat for 8x + 8, where 8x + 8 = 8 * 1, the common factor is 8 so you remove it giving the final simplification of:

4 (x + 7) = 8 (x + 1)