Answer:
B. Infinitely many solutions.
Explanation:
8(x - 4) = 2(4x - 16)
^--This is the original equation.
If we replace x with 1...
we have the same equation, but we add an extra set of brackets. (You'll see why in a second)
8(1 - 4) = 2{4(1) - 16}
1 - 4 = -3
We start by subtracting 4 from 1. When using positive numbers, we can't do this, however. This gets us to -3. leave it in the parenthesis though!
8(-3) = 2{4(1) - 16}
4(1) = 4
Now, the reason we made an extra set of brackets is because 4x is asking you to multiply 4 by x. but as a number, you have to make an extra set of parenthesis to show that. 4 x 1 = 4 so it stays as a 4.
8(-3) = 2(4 - 16)
^-- Now, we are given this new equation. We'll move away from 8(-3) for just a second, to finish the other parenthesis. But still don't remove the parenthesis for 8(-3)!
4 - 16 = -12
We know that 4-16 would also not be possible with positive numbers, but for this equation, as said before.. you're using negative numbers. so 4 - 16 = 12
8(-3) = 2(-12)
^-- And again, we have a new equation. 8(-3) = 2(-12). Don't remove the parenthesis, as I have said before.
8(-3) = -24
Again, the equation shows with parenthesis, it wants us to multiply. Now we take 8, and multiply it by -3. This is a bit tricky, as it is with negative numbers. But in the end, you should have -24.
-24 = 2(-12)
^--The equation becomes -24 = 2(-12). We'll have to multiply again, so keep the parenthesis.
2(-12) = -24
2(-12) Is also asking you to multiply, so now we do the same as before, which again, is a bit tricky because we are using negative numbers. You should end up with -24 though.
-24 = -24
^--Now, you have -24 = -24. This is true since both are the same number.
8(x - 4) = 2(4x - 16)
^-- Here's our wonderful equation again! Let's replace X with a 2 this time!
If you don't understand, read the tips from above to understand what I'm doing in the following equations!
8(2 - 4) = 2{4(2) - 16}
2 - 4 = -2
8(-2) = 2{4(2)-16}
4(2) = 8
8(-2) = 2(8 - 16)
8 - 16 = -8
8(-2) = 2(-8)
8(-2) = -16
-16 = 2(-8)
2(-8) = -16
-16 = -16
And again, we get the same two numbers!
Hope I helped! <3