Let's break down the given expressions step by step.
Left Expression:
\( 2 \cdot \pi \) Since \( \pi \) is slightly greater than 3: \[ 2\pi > 2 \cdot 3 = 6 \]
Right Expression:
The right-hand expression is \( 5 - 2 + 4 + 9 \):
- First simplify \( 5 - 2 \): \[ 5 - 2 = 3 \]
- Now add 4: \[ 3 + 4 = 7 \]
- Finally, add 9: \[ 7 + 9 = 16 \]
Comparison:
Now we have:
- Left Expression: \( 2\pi \) (which is greater than 6)
- Right Expression: \( 16 \)
Now we can compare: \[ 2\pi > 6 < 16 \]
Since \( 2\pi > 6 \) and \( 16 > 6 \), it follows that: \[ 2\pi < 16 \]
Putting it all together, the choices in the blanks would be as follows:
- \( 2\pi \) to \( 6 \)
- \( 6 \) to \( 9 \)
- \( 9 \) to \( 16 \)
Final answer:
- > (2π > 6)
- < (6 < 16)
So, to complete the statements:
- \( 2\pi > 6 \)
- \( 6 < 16 \)
You would select:
- Blank 1: >
- Blank 2: <
- Blank 3: < (6 < 16, comparing 9 to 16 is not needed since it confirms my comparison with the 16)