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
SSSSS [86.1K]
3 years ago
9

How many integers are there in the solution set of the inequality |x−2000|+|x| ≤9999

Mathematics
2 answers:
andriy [413]3 years ago
5 0

Answer:

20,000 integers

Step-by-step explanation:

By triangular inequality,

|x - 2000 + x| ≤ |x−2000|+|x|

|x−2000|+|x| ≤ 9999

|x - 2000 + x| ≤ 9999

|2x - 2000| ≤ 9999

|x - 10000| ≤ 4999.5

x - 10000 ≤ 4999.5

x ≤ 4999.5

x ≤ 14999.5

-(x - 10000) ≤ 4999.5

-4999.5 ≤ x - 10000

-5000.5 ≤ x

All solutions:

-5000.5 ≤ x ≤ 14999.5

No. of inyegers:

14999 - (-5000) + 1

20,000 integers

Fofino [41]3 years ago
3 0

Answer:

9999

Step-by-step explanation:

Find the greatest value of x and the least value of x that satisfy the equation:

2x-2000 = 9999 (Yields the greatest solution)

2x + 2000 = -9999 (Yields the least solution)

Solve both equations and you get:

3999.5 (Greatest solution)

-5999.5 (Least solution)

That means the range of integer solutions is between 3999 and -5999 (inclusive). That means there are 9999 integral solutions

You might be interested in
How to solve 45y to the second power plus 15y minus 10 ?
Lerok [7]

Answer:

Either y =\frac{-2}{3} or, y =\frac{1}{3}

Step-by-step explanation:

We have to solve the following quadratic equation  

45y² + 15y - 10 =0

Now, dividing both sides with 5 we get, 9y² + 3y -2 =0

Hence, to solve the above equation we have to factorize the left-hand part of the equation.

So, 9y² + 3y - 2 =0

⇒ 9y² +6y -3y -2 =0

⇒ (3y +2) (3y -1 ) =0

⇒ Either (3y +2) =0 or (3y -1) =0

⇒ Either y =\frac{-2}{3} or, y =\frac{1}{3} (Answer)

4 0
3 years ago
Plzz helpp I’ll mark brainiest
Andru [333]
Answer is year 3
Ben 19
Amy 22
3 0
2 years ago
Read 2 more answers
Please help me with this problem ASAP
oee [108]

Answer:

Step-by-step explanation:

I think it's 64

8 0
3 years ago
Helpppp I don’t get the question!!!
avanturin [10]

Answer:

43.75    hope i helped you

4 0
3 years ago
What’s the area of the trapezoid?
myrzilka [38]

Answer:

I think its 28 feet

Step-by-step explanation:

2x2=4

3x8=24

24+4=28 ft

7 0
3 years ago
Read 2 more answers
Other questions:
  • Line l contains points (0, -2) and (6, 6). Point P has coordinates (-1, 5)
    12·1 answer
  • SOMEONE PLEASE HELP ME WITH THIS MATH IM STRUGGLING!
    9·1 answer
  • 2 hectometers = centimeters
    12·2 answers
  • If it takes two skilled workers 2 weeks to
    9·1 answer
  • For question 2, find the x- and y-intercept of the line.
    7·1 answer
  • If 120 L of an acid solution is 75% acid, how much pure acid is there<br> in the mixture?
    7·1 answer
  • This is Sample Space. Tyra will flip a red and yellow counter and spin a spinner labeled A-E. if Tyra flips the counter and spin
    12·1 answer
  • At a lunch shop, Aisha buys 2 veggie wraps and 3 apples. Her bill is $14.00. Jaime buys 3 veggie wraps and 2 apples. His bill is
    8·1 answer
  • Car rental company A charges $45 a day to rent a certain car. Car rental B charges $30 a day plus $0.20 per mile to rent a simil
    12·1 answer
  • Pls answer quickly
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!