Question

which symbol in place of the question mark makes the following inequality true for the solutions 4,5,6?
4x ? 16
given:
greater than or equal to
less than or equal to
equal
greater than

Answer 1

To determine which symbol makes the inequality \(4x ? 16\) true for the solutions \(x = 4\), \(x = 5\), and \(x = 6\), we will test each symbol one by one.

1. **Greater than or equal to (≥)**:
\[
4x \geq 16 \implies x \geq 4
\]
For \(x = 4\): \(4 \times 4 = 16\) (True)
For \(x = 5\): \(4 \times 5 = 20\) (True)
For \(x = 6\): \(4 \times 6 = 24\) (True)
This works for all three values.

2. **Less than or equal to (≤)**:
\[
4x \leq 16 \implies x \leq 4
\]
For \(x = 4\): \(4 \times 4 = 16\) (True)
For \(x = 5\): \(4 \times 5 = 20\) (False)
This does not work for \(x = 5\).

3. **Equal (=)**:
\[
4x = 16 \implies x = 4
\]
For \(x = 4\): \(4 \times 4 = 16\) (True)
For \(x = 5\): \(4 \times 5 = 20\) (False)
This does not work for \(x = 5\) or \(x = 6\).

4. **Greater than (>)**:
\[
4x > 16 \implies x > 4
\]
For \(x = 4\): \(4 \times 4 = 16\) (False)
For \(x = 5\): \(4 \times 5 = 20\) (True)
For \(x = 6\): \(4 \times 6 = 24\) (True)
This does not work for \(x = 4\).

The only symbol that makes the inequality \(4x ? 16\) true for all three values \(x = 4\), \(x = 5\), and \(x = 6\) is **greater than or equal to (≥)**.