The number that satisfies the inequality \( \displaystyle\frac{29}{4}\lt\displaystyle\frac{x+20}{4}\lt 8 \) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 3\pi \)
Multiplying all three parts by 4 (a positive number, so the signs stay the same) and then subtracting 20:
\( \displaystyle 29\lt x+20\lt 32 \)
\( \displaystyle 9\lt x\lt 12 \)
Using \( \pi\approx 3.14 \):
\( \displaystyle \frac{\pi}{2}\approx 1.57 \)
\( \pi\approx 3.14 \)
\( 2\pi\approx 6.28 \)
\( 3\pi\approx 9.42 \)
Only \( 3\pi\approx 9.42 \) lies between 9 and 12.