Question

Find the greatest digit that will make each sentence true 648< 48

Answer 1

To find the greatest digit that will make the inequality \(648 < 48\) true, we need to identify the relationship between the two numbers. Currently, the statement is false because 648 is much greater than 48.

If we allow one of the numbers to have a placeholder for a digit (like \(48x\) instead of \(48\), where \(x\) is a digit from 0 to 9), we can rewrite the inequality as \(648 < 48x\).

Now we solve for \(x\):

1. Rewrite the inequality:
\[
648 < 48x
\]

2. Divide both sides by 48 to isolate \(x\):
\[
\frac{648}{48} < x
\]

3. Calculate \(648 ÷ 48\):
\[
648 ÷ 48 = 13.5
\]

Since \(x\) must be a single digit, the smallest integer greater than 13.5 is 14, but \(x\) cannot be 14 since we are limited to digits (0-9). Hence, we can conclude that no digit will make the statement \(648 < 48\) true if we interpret \(48\) as fixed.

If we interpret \(48\) as changing to \(48x\), there is no valid digit \(x\) that can satisfy the initial inequality, as actual possible digits (0-9) do not yield valid results.

Therefore, if you meant to replace \(48\) with a number in the form of \(48y\), \(y\) still has to be 2 or greater for \(48y\) to surpass 648, and thus any digit would not yield truth in the original inequality.

Thus, the answer is that no digit would make \(648 < 48\) true when 48 is treated as a fixed number. If you meant to adjust the inequality into something else, please clarify!