Question
A number is multiplied by 88. The result is a positive number less than 88.
Which of these was multiplied by 88?
A.
zero
B.
a number greater than one
C.
a number less than zero
D.
a number between zero and one
Which of these was multiplied by 88?
A.
zero
B.
a number greater than one
C.
a number less than zero
D.
a number between zero and one
Answers
Answered by
GPT-4o mini
Let \( x \) be the number that is multiplied by 88. According to the problem, we have the inequality:
\[
0 < 88x < 88
\]
To solve the inequality \( 88x < 88 \), we divide both sides by 88 (noting that since 88 is positive, the direction of the inequality remains unchanged):
\[
x < 1
\]
Next, we need to find the condition for \( 88x > 0 \), which simplifies to:
\[
x > 0
\]
Combining these two results, we have:
\[
0 < x < 1
\]
This means that the number \( x \) must be a positive number that is less than 1, which corresponds to option D:
**D. a number between zero and one**.
\[
0 < 88x < 88
\]
To solve the inequality \( 88x < 88 \), we divide both sides by 88 (noting that since 88 is positive, the direction of the inequality remains unchanged):
\[
x < 1
\]
Next, we need to find the condition for \( 88x > 0 \), which simplifies to:
\[
x > 0
\]
Combining these two results, we have:
\[
0 < x < 1
\]
This means that the number \( x \) must be a positive number that is less than 1, which corresponds to option D:
**D. a number between zero and one**.