Question

Which symbol in place of the question mark makes the inequality 2x
? 20 true for the solutions 10, 11, and 12?

Note: you will find the option to add a <
, >
, ≤
, or ≥
symbol in the Comparison (<)
keyboard.

Answer 1

To determine which symbol makes the inequality \(2x \, ? \, 20\) true for the solutions 10, 11, and 12, we can evaluate it for each solution.

1. For \( x = 10 \):
\[
2 \times 10 = 20
\]
We need to check whether \(20\) satisfies the inequality.

2. For \( x = 11 \):
\[
2 \times 11 = 22
\]
Now check if \(22\) satisfies the inequality.

3. For \( x = 12 \):
\[
2 \times 12 = 24
\]
Finally, check if \(24\) satisfies the inequality.

Now, we analyze the possible symbols:

- If we use \( < \):
- \( 20 < 20 \) is false (does not work for \( x = 10\))

- If we use \( > \):
- \( 20 > 20 \) is false (does not work for \( x = 10\))

- If we use \( \leq \):
- \( 20 \leq 20 \) is true (works for \( x = 10\)),
- \( 22 \leq 20 \) is false (does not work for \( x = 11\)),
- \( 24 \leq 20 \) is false (does not work for \( x = 12\))

- If we use \( \geq \):
- \( 20 \geq 20 \) is true (works for \( x = 10\)),
- \( 22 \geq 20 \) is true (works for \( x = 11\)),
- \( 24 \geq 20 \) is true (works for \( x = 12\))

Thus, the symbol that makes the inequality true for all the provided solutions (10, 11, and 12) is \( \geq \).

So, the correct symbol to replace the question mark is:

\[
\geq
\]