Question

Which symbol in place of the question mark make the inequality 2x ? 20 true for the solution 10 11 and 12 note you will find the option to add a < > < or > symbol in the comparison

Answer 1

To determine which symbol to use in the inequality \(2x \, ? \, 20\) for the solutions \(10\), \(11\), and \(12\), we can test each value:

1. **For \(x = 10\)**:
\[
2(10) = 20
\]
This yields the expression \(20 \, ? \, 20\). So, we have:
- \(20 < 20\) (False)
- \(20 > 20\) (False)
- \(20 = 20\) (Not applicable since we're only using \(<\) or \(>\))

2. **For \(x = 11\)**:
\[
2(11) = 22
\]
This yields the expression \(22 \, ? \, 20\). So, we have:
- \(22 < 20\) (False)
- \(22 > 20\) (True)

3. **For \(x = 12\)**:
\[
2(12) = 24
\]
This yields the expression \(24 \, ? \, 20\). So, we have:
- \(24 < 20\) (False)
- \(24 > 20\) (True)

From this, we can conclude that for \(x = 10\), the inequality does not hold for either of the comparison symbols. However, for \(x = 11\) and \(x = 12\), the inequality is true if we use the greater than symbol.

Thus, the correct inequality that holds true for the values \(11\) and \(12\) is:
\[
2x > 20
\]

Therefore, the answer is \(>\).