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In the earlier section we solved equations which contained absolute values. In this section we desire to look at inequalities which contain absolute values. We will have to examine two separate cases.
Inequalities Involving < and ≤
As we did with equations let's begin by looking at a fairly simple case.
p ≤ 4
This says that no matter what p is it ought to have a distance of no more than 4 from the origin. It means that p have to be somewhere in the range,
-4 ≤ p ≤ 4
We could have alike inequality with the < and obtain a similar result.
Generally we have the following formulas to use here,
If |p| ≤ b, b = 0 then - b ≤ p ≤ b
If |p| < b, b =0 then - b < p < b
Find regular grammar for a(a+b)*(ab*+ba*)b
Fact Following any system of equations there are accurately three possibilities for the solution. 1. There will not be a solution. 2. There will be just one solution.
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Example : determine the zeroes of following polynomials. P ( x)= 5x 5 - 20x 4 +5x3 + 50x2 - 20x - 40 = 5 (x + 1) 2 ( x - 2) 3 Solution In this the factoring has been
The United States is becoming more health conscious, and as a result,the problem of obesity has gotten more attention.The Body Mass Index (BMI), relates a person’s height and weigh
First, the standard form of a quadratic equation is ax2 + bx + c = 0 a ≠ 0 Here the only needs are that we have an
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Multiply a Row by a Constant. In this operation we multiply row i by a constant c and the notation will utilizes here is cR i . Note that we can also divide a row by a constant
x+y=0 x=y+4
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