Question

I'm learning algebra with parenthesis and the use of the distributive propety. My Mathematics book gave this as one of the examples:
2(x + 1) - 5(2x - 2)
2 *x + 2 *1 - 5 *2x - 5 *-2 =
2x + 2 - 10x + 10 =
-8x + 12
I pretty much understood everything up to "-8x + 12". I can't even fathom how all of that turned out to be these apparently random numbers...

Answer 1

It's called foiling. So what they did is took the outside number (2) and multiplied it to everything inside of the parenthesis. So that is why they got 2x+2 because 2*x+=2x and 2*1=2. You do the same thing to the other side, so 5*2x=10x and 5*-2=-10. The last part is combining like terms. 2x and -10x both have x's, so you combine them. 2x-10x=-8x. The x just acts as a side component, you can ignore it in the mean time if helps. And then 2+10=12. So the final answer was -8x+12

Answer 2

You leave the x there because they haven't given you a value for x. If they had, for example x=2, then you plug in 2 for x, so -8(2)+12=-16+12=-4

Answer 3

thank you! that helped me so much. I didn't even think about combining the terms afters wards and from both sides of the equation.

Answer 4

As your class continues, they should touch on combining like terms, you will do that for many years!