Question

Which symbol in place of the question mark makes the inequality 2x
? 20 true for the solutions 10, 11, and 12?

Answer 1

To determine which symbol can replace the question mark to make the inequality \(2x \, ? \, 20\) true for the solutions \(x = 10\), \(x = 11\), and \(x = 12\), we will evaluate \(2x\) for these values of \(x\) and check the relationship to \(20\).

1. For \(x = 10\):
\[
2x = 2(10) = 20
\]

2. For \(x = 11\):
\[
2x = 2(11) = 22
\]

3. For \(x = 12\):
\[
2x = 2(12) = 24
\]

Now we check what kind of inequality can hold:

- For \(x = 10\), \(2x = 20\). This means \(2x\) is equal to \(20\).
- For \(x = 11\), \(2x = 22\). This means \(2x\) is greater than \(20\).
- For \(x = 12\), \(2x = 24\). This means \(2x\) is also greater than \(20\).

The values of \(2x\) for \(x = 10\), \(11\), and \(12\) suggest that the appropriate symbol to replace the question mark is \(\geq\) (greater than or equal to).

Thus, the inequality is:
\[
2x \geq 20
\]

This is true for \(x = 10\), \(11\), and \(12\).