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
Find the area of the isosceles triangle
AveGali [126]
175m^2
I got the by multiplying 1/2, by the base (14), by the height (25).

1/2 * 14 * 25
4 0
3 years ago
Read 2 more answers
SOLVE FOR M. please :)
STatiana [176]

Answer:

m =  - 28

Step-by-step explanation:

\frac{ - 3}{7} m = 12

\frac{ - 7}{3} ( \frac{ - 3}{7})m =  \frac{ - 7}{3}  \times 12

\frac{ - 1}{3} ( - 3)m =  \frac{ - 7}{3}  \times 12

- 1( - 1)m =  \frac{ - 7}{3}  \times 12

1 \times m =  \frac{ - 7}{3}  \times 12

m =  \frac{ - 7}{3}  \times 12

m =  \frac{ - 7}{3}  \times 12

m =  \frac{ - 7}{3} (3 \times 4)

m =  - 28

<h3>Hope it is helpful....</h3>
3 0
3 years ago
Alldlyziny Work Tor Errors
stiks02 [169]

Answer: The correct answer is (B)

Step-by-step explanation: No. Ari should have written the percent ratio as 5/100

8 0
3 years ago
Read 2 more answers
Please make Y=x+12 and 4x+2y=27 into one equation.
tiny-mole [99]
So what you need to start with is taking the x from both sides as adding 12 to them. Then, you move the 27 over 4 decimals.
4 0
2 years ago
A roller coaster starts from a deck at an elevation of 20 feet above the ground on the first Hill Climb 78 Feet and then drops 8
GuDViN [60]

Answer:

6 feet above the deck


3 0
3 years ago
Other questions:
  • How does one deal with inequalities again?
    6·1 answer
  • PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
    7·2 answers
  • What is the difference? 1/6 - 5/8 a. -19/24 b. -11/24 c. 11/24 d. 2
    10·1 answer
  • Use the diagram below. Is each statement true?
    13·2 answers
  • Dr. Taylor is a veterinarian. He
    15·1 answer
  • Write the standard equation of a circle with center (-9,-4) and radius 15.
    13·1 answer
  • Simplify the following expression:<br> -13^2=?
    15·1 answer
  • Directions: Find the value of x so that! | m. State the converse used
    14·2 answers
  • I’m stuck on this question
    12·2 answers
  • Parallelogram PQRS with PS = -1 + 4x and QR = 3x + 3. What is the length of QR?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!