I’m not sure of the question your asking here ?
Answer:
<u>The correct answer is B. {-2,4}</u>
Step-by-step explanation:
Let's solve for x, this way:
x + 4/4 = x /x -2
(x + 4) * ((x - 2) = 4 * x
x² - 2x + 4x -8 = 4x
x² - 2x + 4x -8 - 4x = 0
x² - 2x -8 = 0
(x - 4) * (x +2) = 0
x - 4 = 0
x + 2 = 0
x₁ = 4
x₂ = - 2
<u>The correct answer is B. {-2,4}</u>
Since it's so nicely grouped, we can work with it! For the equation to equal 0, x=0, 3, or -1 (since x-3 and x+1 equal 0 when plugged in with 3 and -1 respectively). All we have to do is plug in numbers before, between, and after these numbers and apply it to the rest of them. Since -1 is the smallest number of the group, we can plug in a number below that (for this example, -5) and plug it in to get -8*-5*-4= something negative since it contains an odd number of negative numbers. Therefore, anything less than 1 is negative. For between -1 and 0, we get x=-0.5 equals -0.5*-3.5*0.5=something positive (since it has an even amount of negative numbers), proving that everything between -1 and 0 here is positive. For something between 0 and 3, we can plug 1 in to get 1*-2*2= something negative. Do you see a pattern here? It's negative, then positive, etc.. Therefore, if the number is greater than 3 it is positive. Reviewing a bit, we can see that (-inf, -1) is negative as well as (0,3), making the interval notation (-inf, -1) U (0, 3) since when you plug -1, 0, and 3 in it is 0, not less than 0!
