in the original form, the PRODUCT is less than zero, which means either one or three of the terms is negative.
so, if x<1 works (all three are negative), as does 2<x<3 (one term is negative)
for this inequality:
(x-1)(x-2)(x-3) <0 becomes
x<1 x<2 x<3
but why when I graph the inequality it becomes (this is the actually answer) {x|x<1 or 2<x<3}
I don't understand why it couldn't just be x<3 ?
Also I don't understand why there's an "or" and why the < changed?
4 answers
How would I know its 2<x<3?
the steps to getting x<1 and 2<x<3
When you plotted the graph of the function, did you notice that the graph crosses the x-axis at x=1, x=2 and x=3?
The graph stays below the x-axis when x<1, and also when 2<x<3.
x<1 when all three factors are negative, and 2<x<3 when only one term (x-3) is negative, as Mr. Pursley mentioned.
The graph stays below the x-axis when x<1, and also when 2<x<3.
x<1 when all three factors are negative, and 2<x<3 when only one term (x-3) is negative, as Mr. Pursley mentioned.
1 answer