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

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esfloravaou · Accepted Answer

Assume&amp;nbsp;x∈R.&amp;nbsp;The distance of x from 6 - |x−6|.&amp;nbsp;The distance is equal to 4.&amp;nbsp;The required equation is |x−6|=4.&amp;nbsp;|x-6|=4&amp;nbsp;-4&amp;lt;x-6&amp;lt;4&amp;nbsp;-4+6&amp;lt;x-6+6&amp;lt;4+6&amp;nbsp;2&amp;lt;x&amp;lt;10&amp;nbsp;The required numbers are 2 and 10.

karton · Accepted Answer

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:|x−6|=4This 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: x−6≥0If x−6≥0, then |x−6|=x−6. Substituting this into the equation, we have:x−6=4Solving for x, we find:x=10Therefore, x=10 is a solution in this equation.Equation 2: x−6&amp;lt;0If x−6&amp;lt;0, then |x−6|=−(x−6). Substituting this into the equation, we have:−(x−6)=4Solving for x, we find:x=2Therefore, x=2 is a solution in this equation.Hence, the solutions to the equation |x−6|=4 are x=2 and x=10.|x−6|=4x−6=4x=10−(x−6)=4x=2

star233 · Accepted Answer

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:|x−6|=4This 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 &amp;gt; 0In this case, we have:x−6=4Solving for x, we get:x=4+6x=10Case 2: x - 6 &amp;lt; 0In this case, we have:−(x−6)=4Multiplying both sides by -1, we get:x−6=−4Solving for x, we get:x=−4+6x=2Therefore, the numbers x that are at a distance of 4 from the number 6 are 10 and 2.

user_27qwe · Accepted Answer

Result:x = 10 and x = 2Solution:|x−6|=4This 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) = 4In this case, the difference between x and 6 is positive 4. Solving for x, we have:x−6=4x=4+6x=10Case 2: -(x - 6) = 4In this case, the difference between x and 6 is negative 4. Solving for x, we have:−(x−6)=4−x+6=4−x=4−6−x=−2x=−(−2)x=2Therefore, the solutions to the equation |x - 6| = 4 are x = 10 and x = 2.

Describe all numbers x that are at a distance of

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