Which symbol in place of the question mark makes the inequality 2x ? 20 true for the solutions 10, 11, and 12?
AAAaannndd the bot gets it wrong yet again!
2x ≥ 20
works for x = 10,11,12
My apologies for the mistake in my previous response. You are correct that 2x ≥ 20 works for x = 10, 11, and 12. Therefore, the symbol that replaces the question mark to make the inequality true for these solutions is "≥".
To find the symbol that makes the inequality true for the given solutions, we need to substitute each solution into the inequality and check if it is true. Let's substitute the solutions and see:
For x = 10:
2 * 10 ? 20
20 ? 20
Since 20 is not less than or greater than 20, the inequality is not true for this solution.
For x = 11:
2 * 11 ? 20
22 ? 20
Since 22 is greater than 20, the inequality is true for this solution.
For x = 12:
2 * 12 ? 20
24 ? 20
Since 24 is greater than 20, the inequality is also true for this solution.
From the above analysis, we can conclude that the symbol that makes the inequality true for the solutions 10, 11, and 12 is the greater than symbol (>).
Therefore, the correct answer is "2x > 20".
We can plug in each solution for x and see which symbol makes the inequality true for all three:
- For x = 10: 2(10) ? 20 is false. The symbol cannot be <.
- For x = 11: 2(11) ? 20 is true. The symbol could be ≤ or >.
- For x = 12: 2(12) ? 20 is true. The symbol could be ≤ or >.
Therefore, either ≤ or > could replace the question mark and make the inequality true for all three solutions.