To solve the inequality [tex]\(-20.2 > 0y\)[/tex], let's break it down step-by-step.
1. Inequality Simplification:
The given inequality is:
[tex]\[-20.2 > 0y\][/tex]
Since [tex]\(0 \times y = 0\)[/tex], the inequality simplifies to:
[tex]\[-20.2 > 0\][/tex]
2. Analyzing the Simplified Inequality:
Now, evaluate the inequality [tex]\(-20.2 > 0\)[/tex]:
- The statement [tex]\(-20.2 > 0\)[/tex] is false because [tex]\(-20.2\)[/tex] is less than 0.
3. Checking Possible Statements:
Now we will analyze each of the provided statements to determine which must be true:
- Statement 1: You cannot divide by zero.
This statement is true as a general mathematical rule; division by zero is undefined.
- Statement 2: The inequality is equivalent to [tex]\(-20.2 > 0\)[/tex], which is false.
This is true because we simplified [tex]\(-20.2 > 0y\)[/tex] to [tex]\(-20.2 > 0\)[/tex], and [tex]\(-20.2 > 0\)[/tex] is indeed false.
- Statement 3: The solution is [tex]\(y > 0\)[/tex].
This statement would imply that the inequality holds for [tex]\(y > 0\)[/tex]. However, we have established that the simplified inequality is false, so there is no value of [tex]\(y\)[/tex] that makes it true.
- Statement 4: The solution is [tex]\(0 > y\)[/tex].
Similar to the previous statement, this implies that the inequality holds for [tex]\(0 > y\)[/tex], which is also incorrect given that the simplified inequality is false.
- Statement 5: The solution is [tex]\(y = 0\)[/tex].
This implies that the inequality holds when [tex]\(y = 0\)[/tex]. Again, this is incorrect because the inequality [tex]\(-20.2 > 0\)[/tex] is false regardless of [tex]\(y\)[/tex]'s value.
4. Conclusion:
The correct statements that must be true are:
- Statement 1: You cannot divide by zero.
- Statement 2: The inequality is equivalent to [tex]\(-20.2 > 0\)[/tex], which is false.
Therefore, the answer is:
[tex]\[ [1, 2] \][/tex]
