Carlson Allan
03/01/2024 · Junior High School
11. If the sum of half a number and 3 is smaller than twice the same number added to 3 , which of the following could be the number?
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Let's denote the unknown number as \( x \). According to the problem, we can set up the following inequality based on the given conditions:
\[
\frac{1}{2}x + 3 < 2x + 3
\]
Now, we can simplify this inequality:
1. Subtract 3 from both sides:
\[
\frac{1}{2}x < 2x
\]
2. Next, subtract \(\frac{1}{2}x\) from both sides:
\[
0 < 2x - \frac{1}{2}x
\]
3. Combine the terms on the right side:
\[
0 < \frac{4}{2}x - \frac{1}{2}x
\]
\[
0 < \frac{3}{2}x
\]
4. To isolate \( x \), multiply both sides by \(\frac{2}{3}\) (note that since \(\frac{2}{3}\) is positive, the inequality direction remains the same):
\[
0 < x
\]
This means that \( x \) must be a positive number.
Thus, any positive number could satisfy the original condition. If you have specific options to choose from, any positive number from those options would be a valid answer.
Quick Answer
\( x \) must be a positive number.
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