Question

Which symbol in place of the question mark makes the following inequality true for the solutions 4 5 6
4x ? 16

>
>=
<=
=

Answer 1

To determine which symbol makes the inequality \( 4x \, ? \, 16 \) true for the solutions \( x = 4, 5, 6 \), we can evaluate each case with the different symbols:

1. **Using \( > \)**:
- For \( x = 4 \): \( 4(4) = 16 \) → \( 16 > 16 \) (**False**)
- For \( x = 5 \): \( 4(5) = 20 \) → \( 20 > 16 \) (**True**)
- For \( x = 6 \): \( 4(6) = 24 \) → \( 24 > 16 \) (**True**)

So, \( > \) is **not valid** since it fails for \( x = 4 \).

2. **Using \( >= \)**:
- For \( x = 4 \): \( 4(4) = 16 \) → \( 16 >= 16 \) (**True**)
- For \( x = 5 \): \( 4(5) = 20 \) → \( 20 >= 16 \) (**True**)
- For \( x = 6 \): \( 4(6) = 24 \) → \( 24 >= 16 \) (**True**)

So, \( >= \) is **valid** for all solutions.

3. **Using \( <= \)**:
- For \( x = 4 \): \( 4(4) = 16 \) → \( 16 <= 16 \) (**True**)
- For \( x = 5 \): \( 4(5) = 20 \) → \( 20 <= 16 \) (**False**)
- For \( x = 6 \): \( 4(6) = 24 \) → \( 24 <= 16 \) (**False**)

So, \( <= \) is **not valid** since it fails for \( x = 5 \) and \( x = 6 \).

4. **Using \( = \)**:
- For \( x = 4 \): \( 4(4) = 16 \) → \( 16 = 16 \) (**True**)
- For \( x = 5 \): \( 4(5) = 20 \) → \( 20 = 16 \) (**False**)
- For \( x = 6 \): \( 4(6) = 24 \) → \( 24 = 16 \) (**False**)

So, \( = \) is **not valid** since it fails for \( x = 5 \) and \( x = 6 \).

Therefore, the only symbol that makes the inequality true for all three solutions \( x = 4, 5, 6 \) is \( \geq \).

So, the answer is:
**>=**