Question

4 ( 2x-2 ) +2 = 4 ( x- 2 )

Answer 1

`x=-(1)/(2)`

Explanation:

`4(2x-2)+2=4(x-2)`

• First, let's go over the distributive property in math. When you have any expression within a parenthesis being multiplied by any expression outside a parenthesis, you are distributing the values outside onto the values inside, like so:
• 
  `a(b+c)` ⇒
  `ab+ac`
• Hopefully this helps you break down how distribution works, but if you're still having trouble comprehending it, looking at examples will help. Now, back to the problem. Let's try this idea of distribution on the left side of the equation.

`4(2x-2)+2=4(x-2)\\((4)2x-(4)2)+2=4(x-2)\\(8x-8)+2=4(x-2)`

• Hopefully you could follow this math, but if not, there are plenty of materials online and in books on this. Be sure to look at those if you still have trouble.
• Now that we have done all the multiplication we can on the left side and only addition and subtraction remain, we can get rid of the parentheses.

`(8x-8)+2=4(x-2)\\8x-8+2=4(x-2)\\8x-6=4(x-2)`

• Now let's do distribution for the other side as well. Doing this will help us easily isolate
  `x` on one side after.

`8x-6=4(x-2)\\8x-6=((4)x-(4)2)\\8x-6=4x-8`

• Now, using addition and subtraction, let's move all our
  `x` values to one side of our equation and all other values to the other. It doesn't matter which side you choose.

`8x-6=4x-8\\4x=-2\\(4x)/(4)=(-2)/(4)`

• In case you're confused by the last step there, what I did was divide both sides by the coefficient in front of our
  `x` values. This will cancel the coefficient out and leave us with our solution.

`(4x)/(4)=(-2)/(4)\\x=(-1)/(2)=-(1)/(2)`

• The fraction
  `(-2)/(4)` is technically correct, but it isn't simplified.
  `(-2)/(4)` can be simplified to
  `-(1)/(2)`, so
  `-(1)/(2)` is our final answer.

`x=-(1)/(2)`