Question

Which symbol in place of the question mark makes the inequality 2x ? 20 true for the solutions 10, 11, 12
Substitute in 10 11 and 12 individually
Ex 2 (10) =?, then 2 (11) =?, then 2 (12) =?
Then pick the inequality sign that makes all three statements true
<
>
<=
>=

Answer 1

To determine the appropriate inequality symbol to replace the question mark in the inequality \(2x \, ? \, 20\) that makes it true for \(x = 10\), \(x = 11\), and \(x = 12\), we need to evaluate the inequality for each value of \(x\).

Let's substitute each value into \(2x\) and compare it to \(20\):

1. For \(x = 10\):
\[
2(10) = 20
\]
- We need to check \(20 \, ? \, 20\).

2. For \(x = 11\):
\[
2(11) = 22
\]
- We need to check \(22 \, ? \, 20\).

3. For \(x = 12\):
\[
2(12) = 24
\]
- We need to check \(24 \, ? \, 20\).

Now, let's check each inequality symbol:

1. **Using \(<\)**:
- \(20 < 20\) (False)
- \(22 < 20\) (False)
- \(24 < 20\) (False)

2. **Using \(>\)**:
- \(20 > 20\) (False)
- \(22 > 20\) (True)
- \(24 > 20\) (True)

3. **Using \(<=\)**:
- \(20 <= 20\) (True)
- \(22 <= 20\) (False)
- \(24 <= 20\) (False)

4. **Using \(>=\)**:
- \(20 >= 20\) (True)
- \(22 >= 20\) (True)
- \(24 >= 20\) (True)

Based on the analysis, the only inequality that holds true for all three \(x\) values (10, 11, and 12) is \( \geq \).

So the correct symbol to replace the question mark is \( \geq \):
\[
2x \geq 20
\]