Well, that's how I do it:
Expanding and simplifying,
Now, since x^2 - 2x + 4 < 0 has no real solutions,
x(x-4) < 0
The critical values are x = 0 and x = 4.
I do my table, and get as answer: 0 < x < 4.
First of all, does anyone know where I can find an explanation of these types of questions on the internet? I've never solved absolute value questions before so I don't know exactly what to do. And my book just solves the question but doesn't explain it at all...
I understand this much:
And from here I don't understand - the book starts answering the question by the boundaries:
(i) for
the inequality and this inequality produces
So I won't continue the rest of the answer. If I understand this part I assume I'll understand the rest. How did they get (i) as the boundary? Where did that inequality come from??
Hello, jayshizwiz!
How about a graphic solution?
The graph of
. . is an up-opening parabola with -intercepts 1 and 2.
Its graph looks like this:
Code:| *| * | | * * | |* * | * * - - + - * - - - - - - * - - - - | 1 * * 2 | * |
The graph of looks like this:
Everything below the -axis is reflected upward.Code:| o| o | | o o | |o o o | o o o o - - - + - o - - - - - - o - - - - | 1 2 |
The graph of looks like this:Code:| | * | * | * | * 2| * * * | * | * | - - * - - - + - - - - - - * -2 | * | |
The graph of looks like this:
Code:| | ∆ | ∆ | ∆ | ∆ | ∆ ∆ ∆ | ∆ ∆ | ∆ ∆ | - - ∆ - - - + - - - - - - -2 |
Sketch the two graphs on a set of coordinate axes.
Code:| o | ♥(4,6) | ∆ | ∆ | ∆ | ∆ | ∆ o | ∆ o | ∆ | ∆ | ∆ o| ∆ o | ∆ (0,2)| ∆ ♥ o ∆ | ∆ ∆ |o o o ∆ ∆ | o o o o - - ∆ . . - + - o - - - - - - o - - - - -2 | 1 2 |
When is the "parabola" below the "line"?
Answer: .
Well, you can see the graph now. The graph of |x+2| is above that of |x^2 - 3x + 2| only within that range.
When you go towards the left, the parabolic part of |x^2 - 3x + 2| goes up 'faster' than the graph of |x+2|, hence, |x+2| will never be above the parabola again.
The same thing occurs on the right.