To determine which of the given options are solutions to the equation \(\(1x = 0\)\), we need to evaluate each option separately and see if they satisfy the equation.
The given equation \(\(1x = 0\)\) simplifies to \(\(x = 0\)\).
Let's assess each option:
Option A: 0
- Substituting \(\(x = 0\)\) into the equation \(\(1x = 0\)\):
\(\[
1 \times 0 = 0
\]\)
This is true since \(\(0 = 0\)\). Therefore, 0 is indeed a solution.
Option B: All positive numbers
- Consider any positive number, for example, \(\(x = 1\)\):
\(\[
1 \times 1 = 1
\]\)
This is false because \(\(1
eq 0\)\). Therefore, not all positive numbers can be solutions.
Option C: All negative numbers
- Consider any negative number, for example, \(\(x = -1\)\):
\(\[
1 \times -1 = -1
\]\)
This is false because \(\(-1
eq 0\)\). Therefore, no negative numbers can be solutions.
Option D: None of these
- This option is incorrect because we identified that 0 is indeed a solution from Option A.
Based on this evaluation, the solutions to the equation \(\(1x = 0\)\) are:
A. 0 ☐
B. All positive numbers
C. All negative numbers
D. None of these
