1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
A car's wheels spins at 1000 revolutions per minute. The diameter of the wheels is 23 inches. You want to know how fast the car
ch4aika [34]

Answer:

72,220 inches per  minute

Step-by-step explanation:

A car's wheels spins at 1000 revolutions per minute. The diameter of the wheels is 23 inches.

1 revolution = 2\pi radians

\frac{theta}{tome}=\frac{1000 \ revolution}{1 \ minuite} = \frac{1000* 2\pi }{1} =\frac{2000\pi}{1 \ minute}

Speed V= \frac{r*theta}{t}

r is the radius , theta is the angle and t is the time

We know diameter = 23  , then radius = 23/2

Speed V= \frac{23}{2}*\frac{2000\pi}{1}

Value of pi = 3.14

speed = 23000* 3.14= 72220 inches/ minute


3 0
3 years ago
Read 2 more answers
Twelve out of 18 students in Mrs. Marlin's class buys pizza for lunch on Fridays.at this rate,if there are 240 students in the e
Bond [772]

I believe it’s 80 but I’m not sure

8 0
3 years ago
To find the quotient of 8 divided by one-third, multiply 8 by
likoan [24]

Answer:

3

Step-by-step explanation:

Skip,Flip,Multiply Method

\frac{8}{ \frac{1}{3} }  =  \frac{8}{1}  \times 3 = 24

4 0
3 years ago
Read 2 more answers
Helppp mehh plzz..............
soldier1979 [14.2K]

Answer:

i think it A

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A musician purchases a pair of cube-shaped speakers that are 9 inches across. If the face of the speaker takes up of the total v
netineya [11]

Answer:

Assuming "the speaker takes up 1/6 of the internal volume"

volume is 9³ in³

you want the remaining volume, which is 5/6 of the total

(5/6)9³ = 607.5 in³

double that if you want the remaining volume for BOTH speakers....

3 0
3 years ago
Other questions:
  • Misty has 36 pairs of shoes arranged on a number of shelves
    7·1 answer
  • How do I know if it's a function or not?
    15·2 answers
  • Need help with this, thank you!!!!
    11·1 answer
  • Help please. Jskskfkfkrkejekejwheheheehehe
    11·1 answer
  • Plz help. A tram moved upward 3 meters per second for 24 seconds. What was the total change in the tram's elevation?
    8·1 answer
  • 4. Determine the following for the equation y = vx – 1.
    6·1 answer
  • What is the answer for this question
    9·1 answer
  • A culture started with 1,000 bacteria. After 6 hours it grew to 1,100 bacteria. Predict how many bacteria will be present after
    15·1 answer
  • Please someone help it’s for a test that is due sooooonnn
    8·2 answers
  • Solve the system by substitution.<br> 3x + y = 20<br> -7y=x<br><br> Please help
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!