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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
Maximise, p =168x+161y+158z+132w 475x+450y+440z+438w 250x+230y+220z+210w 119x+115.5y+114.8z+112.25w 160x+50y+120z+50w 12x+8.8y+7.4z+5.3w x >=4
2-1-f+7=
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Horizontal Shifts These are quite simple as well though there is one bit where we have to be careful. Given the graph of f ( x ) the graph of g ( x ) = f ( x + c ) will be t
Example: Solve following. | 10 x - 3 |= 0 Solution Let's approach this one through a geometric standpoint. It is saying that the quantity in th
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1/1+x+1/y+1/1+z+1/x+1/1+y+1/z=1
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