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Delvig [45]
3 years ago
11

Explain the rule in solving inequalities with a negative coefficient.

Mathematics
1 answer:
dimulka [17.4K]3 years ago
7 0

Answer:

  the comparison must be reversed when multiplying by a negative

Step-by-step explanation:

The rules of equality apply to solving inequalities, with the exception that multiplication or division by a negative number reverses the sense of the comparison:

  -x > 1

  x < -1 . . . . . multiply both sides by -1

____

Effectively, multiplication (or division) by a negative number is equivalent to reflection across the origin. Things that were ordered left/right (on the number line) are ordered right/left after such a reflection:

  -2 < -1

  1 < 2

_____

<em>Additional comment</em>

Application of any function requires that you pay attention to ordering. Some functions naturally reverse the order; others do so only on specific domains.

Consider f(x) = 1/x.

  1 < 2

  f(1) > f(2) . . . . because the slope of the f(x) function is negative everywhere.

__

<em>In the first and second quadrants</em>, the cosine function also reverses order.

  20° > 10°

  cos(20°) < cos(10°)

__

Probably the most commonly encountered function used with inequalities is the absolute value function.

  |x-3| > 2

This function has one domain where the slope is negative, and another domain where the slope is positive.

  For x < 3, the function negates its argument, so we have ...

     -(x -3) > 2

     -x +3 > 2

     -x > -1

     x < 1 . . . . . everywhere consistent with x < 3

  For x ≥ 3, the function does nothing, so we have ...

     x -3 > 2

     x > 5

  The solution to this absolute value inequality is (x < 1) ∪ (x > 5).

__

You can also resolve negative coefficients by adding the opposite. Addition and subtraction never require any change to the comparison operator.

  -x > 1

  0 > x +1 . . . . x is added

  -1 > x . . . . . . -1 is added

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irakobra [83]

The top portion of this graph would be y = 4

The bottom portion would be y = x - 1


In order to find both of these, we have to look at them separately. Let's start with the flat line between 1 and -1. Since it is between those numbers, we know this one goes on top. We also know that since the line is horizontal, that the equation must be y = the number that it sits at. This is the definition of a horizontal line. Since the line is at 4, we get y = 4.


For the sloped portion, we have to pick two points and find the equation of the line. Let's use (3, 2) and (5, 4). We must start by finding slope (m)


m = (y1 - y2)/(x1 - x2)

m = (4 - 2)(5 - 3)

m = 2/2

m = 1


So we know slope to equal 1. Now we can use a point and slope intercept form to find the y-intercept (b)


y = mx + b

4 = 1(5) + b

4 = 5 + b

-1 = b


Now put them together in an equation for the bottom part: y = x - 1

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3 years ago
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Vanyuwa [196]
You’re solving for the volume of the cylinder. so the way you would do this is the area of the base of the cylinder (pi times radius squared) which in this case would be 3.14 x 10^2 which is 314. you would then multiply by h, the height, which here is 10. 314 x 10 is 3140.
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3 years ago
Can someone help me with this
melisa1 [442]
First part
option 2 p=KB

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7 0
1 year ago
Graph the function h(t)= 7t-175
Nataly [62]
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3 years ago
The observations of 124.53, 124.55, 142.51, and 124.52 are obtained when taping the length of a line. What should the observer c
mylen [45]

Answer: the observer should consider to eliminate or to retake the third measure.

Explanation:

The four measures taken are 124.53, 124.55, 142.51 and 124.52.

As it can be easily seen, the third measure is much different from the other three. This means that something went wrong during the observation: it can be either the measure taken wrong or that the number was written wrong (if you switch the 2 and the 4 you get a number similar to the other ones).

If the third measure is not considered, an estimate of the mean would place it around 124.5, while if the outlier (the detatched number) is considered an estimate of the mean would increase to about 129.

Therefore, in order to obtain a more reliable mean, the observer should consider to eliminate or to retake the third measure.

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