Describe all numbers x that are at a distance of

Lennie Davis

Lennie Davis

Answered question

2021-12-10

Describe all numbers x that are at a distance of 4 from the number 6. Express this using absolute value notation.

Answer & Explanation

esfloravaou

esfloravaou

Beginner2021-12-11Added 43 answers

Assume xR
The distance of x from 6 - |x−6|. 
The distance is equal to 4. 
The required equation is |x−6|=4. 
|x-6|=4 
-4<x-6<4 
-4+6<x-6+6<4+6 
2<x<10 
The required numbers are 2 and 10.

karton

karton

Expert2023-05-22Added 613 answers

The absolute value of a number x, denoted as |x|, represents the distance between x and zero on the number line. In this case, we want to find the numbers that are at a distance of 4 from the number 6.
Using the absolute value notation, we can express this as:
|x6|=4
This equation states that the absolute value of the difference between x and 6 is equal to 4.
To solve this equation, we can consider two equation:
Equation 1: x60
If x60, then |x6|=x6. Substituting this into the equation, we have:
x6=4
Solving for x, we find:
x=10
Therefore, x=10 is a solution in this equation.
Equation 2: x6<0
If x6<0, then |x6|=(x6). Substituting this into the equation, we have:
(x6)=4
Solving for x, we find:
x=2
Therefore, x=2 is a solution in this equation.
Hence, the solutions to the equation |x6|=4 are x=2 and x=10.
|x6|=4
x6=4
x=10
(x6)=4
x=2
star233

star233

Skilled2023-05-22Added 403 answers

To describe all numbers x that are at a distance of 4 from the number 6 using absolute value notation, we can express it as:
|x6|=4
This equation states that the absolute value of the difference between x and 6 is equal to 4. To find the values of x that satisfy this equation, we can set up two cases: one where x - 6 is positive and one where x - 6 is negative.
Case 1: x - 6 > 0
In this case, we have:
x6=4
Solving for x, we get:
x=4+6
x=10
Case 2: x - 6 < 0
In this case, we have:
(x6)=4
Multiplying both sides by -1, we get:
x6=4
Solving for x, we get:
x=4+6
x=2
Therefore, the numbers x that are at a distance of 4 from the number 6 are 10 and 2.
user_27qwe

user_27qwe

Skilled2023-05-22Added 375 answers

Result:
x = 10 and x = 2
Solution:
|x6|=4
This equation represents the absolute value of the difference between x and 6, which should be equal to 4. To find the values of x that satisfy this equation, we can set up two cases:
Case 1: (x - 6) = 4
In this case, the difference between x and 6 is positive 4. Solving for x, we have:
x6=4
x=4+6
x=10
Case 2: -(x - 6) = 4
In this case, the difference between x and 6 is negative 4. Solving for x, we have:
(x6)=4
x+6=4
x=46
x=2
x=(2)
x=2
Therefore, the solutions to the equation |x - 6| = 4 are x = 10 and x = 2.

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