Find the greatest digit that will make each sentence true 4839> 839

1 answer

To determine the greatest digit that can replace a variable in "4839 > 839" such that the inequality remains true, we need to analyze the components of the expression.

The numerical inequality "4839 > 839" is true because 4839 is indeed greater than 839.

If we introduce a variable (let’s say "x") that represents a digit to be placed in either number, we can analyze the inequality:

  1. If "x" replaces a digit in "4839", the largest possible value for each digit is 9, meaning we need to see what replacing a digit does to the inequality.

  2. If we replace the last digit (3) of 4839 with a variable "x":

    • We would have the inequality 4849 > 839.
    • This is true for any digit "x" from 0 to 9, as they all yield a value greater than 839.
  3. If we replace "4" in 4839 with "x", where "x" can only be a digit from 0 - 9:

    • If x = 0, we get 0839, which is not greater than 839.
    • So, "x" could be 1, 2, 3 to keep 1xxx greater than 839.
    • However, the goal here is to find the greatest digit.
  4. If we change “8” from 4839 to “x”, we see that we must keep the left side greater than 839. The smallest possible value that "x" can be, to keep 4x39 > 839, must be calculated. For example:

    • If x = 9, we have 4939 > 839 (true).
    • If x = 8, we have 4839 > 839 (true).
    • If x = 0, we have 4039 > 839 (true).

Lastly:

  1. To find the "greatest digit" in general, the variables can keep the current order and function - meaning replacing, keeping the value of "x" consistent while adhering to 0-9 rule would not sway the current logic of truth in the greater than side.

Thus, placing the value of the variables accordingly, the greatest digit leading to a true statement ultimately remains 9 achieving the deepest end of the greatest possibility in the value placement.

To summarize, if we analyze this while keeping "certain digits intact", that leads to concluding "greatest integer" being 9 itself. Thus, no values lower than that bring this definition of 'truth' into question.

So, the final answer is 9.