SOLUTION: What makes answer choice A and B different on a number line? Never mind the number line if you can't understand it, but I know that answer A is correct, but why not answer B?
<=
Algebra ->
Number-Line
-> SOLUTION: What makes answer choice A and B different on a number line? Never mind the number line if you can't understand it, but I know that answer A is correct, but why not answer B?
<=
Log On
Question 1083297: What makes answer choice A and B different on a number line? Never mind the number line if you can't understand it, but I know that answer A is correct, but why not answer B?
<==4--3--2--1--0--1========>
A) (x-1)(x+4)>0
B) (x-1)(x+4)<0 Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! Set (x-1)(x+4) equal to zero and solve for x. The two solutions are x = 1 or x = -4. Plot -4 and 1 on the number line. Mark the regions between and around the points P, Q, and R as you see below
Pick a representative point from the red region P. One such value is x = -6. Plug this into the expression (x-1)(x+4) to get
(x-1)(x+4) = (-6-1)(-6+4) = (-7)*(-2) = 14
This result is positive, so (x-1)(x+4) > 0 for any point in the red region
--------------
Repeat for the blue region Q. Pick something like x = -2
(x-1)(x+4) = (-2-1)(-2+4) = (-3)*(2) = -6
So (x-1)(x+4) < 0 for the blue region
---------------
Repeat for the green region R
Pick something like x = 3
(x-1)(x+4) = (3-1)*(3+4) = (2)*(7) = 14
So (x-1)(x+4) > 0 for the green region
-----------------------------------
In summary, (x-1)(x+4) > 0 if you pick an x value from either the red region P or from the green region R
(x-1)(x+4) < 0 is true if you pick a point from the blue region Q
-----------------------------------
Note: plugging either x = -4 or x = 1 leads to (x-1)(x+4) being 0 so (x-1)(x+4) > 0 nor (x-1)(x+4) < 0 is true.
(
