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Comment on Quadratic Inequality with x
If we end up picking the
For the purposes of this
For the purposes of this question, we can stop once we find a negative result (x = -2).
I just wanted to follow through with the entire solution to reinforce the approach described in the previous lesson (https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...)
Is it always the middle
No, definitely not.
No, definitely not.
Isn't it an overkill to solve
Unless you can show me an example where the value of x is outside the range of the solution resulting from setting the expression to zero, I have to say that it is a total waste of time graphing the solution on the number line. That's just my take.
The number line can be used
The number line can be used to organize ones thoughts. If you find that you don't need to use one, that will save you some time.
In some cases, (like in a Quantitative Comparison question), there can be more than one range of values that satisfy the inequality, in which case, you might find it useful to use the number line.
In addition to what you've
If we had a negative value in front of x, like -x2 − 8x − 7, things would be opposite, as our parabola would open down. The region between the y=0 values would be positive, and outside of the y=0 areas would be negative.
I presume we can also say that since the inequality is <0 in this case that we know that the bottom of the parabola will fall below the y axis.
If you have a cubic equation or higher, then I guess you do have to test each region.
So, looking at your explanation and the mathisfun one together it all seems to make sense.
I guess my point is it might help people if they remember that a quadratic equation will always be a parabola and that this problem can also be thought of graphically. (Of course maybe everyone else does keep that in mind).
Those are great points, Kevin
Those are great points, Kevin! Thanks for that.
Cheers,
Brent
I didn't use number line to
--> x^2 - 4x + 3 + 1 - 1 < 0
--> (x^2 - 4x + 4) - 1 < 0
--> (x-2)^2 - 1 < 0
--> (x-2)^2 < 1
The only way for this equation to be less than one is when x = 2
Perfect. You used a technique
Perfect. You used a technique called" completing the square" to eventually get the inequality (x-2)^2 < 1
Hi Brent, so we found out is
We're not saying x is
We're not saying x is negative.
We are saying saying that, if 1 < x < 3, then the value of x² - 4x + 3 is negative.