What expression is equivalent to 1/4 (x+24)
2 answers:
<h3>hello!
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</h3>
Use the Distributive Property, which states the following:-
Where
we distribute a by multiplying it times b and c
a, b, and c can be either constants (numbers) or variables (letters)
Distribute:-
Multiply the term before the parentheses by the terms inside the parentheses:-
Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
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Answer:
.
Step-by-step explanation:
See below for a proof of why all but the first digit of this must be "
".
Taking that lemma as a fact, assume that there are digits in
after the first digit,
:
, where
is a positive integer.
Sum of these digits:
.
Since is a digit, it must be an integer between
and
. The only possible value that would ensure
is
and
.
Therefore:
.
.
.
Hence, the sum of the digits of would be
.
Lemma: all digits of this other than the first digit must be "
".
Proof:
The question assumes that is the smallest positive integer whose sum of digits is
. Assume by contradiction that the claim is not true, such that at least one of the non-leading digits of
is not "
".
For example: , where
,
,
, and
are digits. (It is easy to show that
contains at least
digits.) Assume that
is one of the non-leading non-"
" digits.
Either of the following must be true:
, the digit in front of
is a "
", or
If , the digit in front of
, is a "
", then let
be
with that "
" digit deleted:
.
The digits of would still add up to
:
.
However, with one fewer digit, . This observation would contradict the assumption that
is the smallest positive integer whose digits add up to
.
On the other hand, if , the digit in front of
, is not "
", then
would still be a digit.
Since is not the digit
,
would also be a digit.
let be
with digit
replaced with
, and
replaced with
:
.
The digits of would still add up to
:
.
However, with a smaller digit in place of ,
. This observation would also contradict the assumption that
is the smallest positive integer whose digits add up to
.
Either way, there would be a contradiction. Hence, the claim is verified: all digits of this other than the first digit must be "
".
Therefore, would be in the form:
, where
, the leading digit, could also be
.