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.

(1 point)

Answer 1

To determine the correct symbol to replace the question mark in the inequality \( 2x \, ? \, 20 \) that makes the statement true for the solutions 10, 11, and 12, we can evaluate each option:

1. For \( x = 10 \):
- \( 2(10) = 20 \)
2. For \( x = 11 \):
- \( 2(11) = 22 \)
3. For \( x = 12 \):
- \( 2(12) = 24 \)

Now, we can evaluate the inequality options one by one:

- If we use \( < \):
- \( 20 < 20 \) (false for \( x = 10 \))
- \( 22 < 20 \) (false for \( x = 11 \))
- \( 24 < 20 \) (false for \( x = 12 \))

- If we use \( > \):
- \( 20 > 20 \) (false for \( x = 10 \))
- \( 22 > 20 \) (true for \( x = 11 \))
- \( 24 > 20 \) (true for \( x = 12 \))

- If we use \( ≤ \):
- \( 20 ≤ 20 \) (true for \( x = 10 \))
- \( 22 ≤ 20 \) (false for \( x = 11 \))
- \( 24 ≤ 20 \) (false for \( x = 12 \))

- If we use \( ≥ \):
- \( 20 ≥ 20 \) (true for \( x = 10 \))
- \( 22 ≥ 20 \) (true for \( x = 11 \))
- \( 24 ≥ 20 \) (true for \( x = 12 \))

The only symbol that makes the inequality true for all solutions (10, 11, and 12) is \( ≥ \).

So, the correct symbol to use is:
\( \geq \)