Which symbol in place of the question mark makes the inequality 2x

Question

? 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 which symbol in place of the question mark makes the inequality \( 2x , ? , 20 \) true for the solutions 10, 11, and 12, we can evaluate \( 2x \) for these values:

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

Now let's evaluate the inequality \( 2x , ? , 20 \):

• For \( x = 10 \): \( 20 , ? , 20 \) → This is true if we use \( \leq \) or \( = \).
• For \( x = 11 \): \( 22 , ? , 20 \) → This is true if we use \( > \) or \( \geq \).
• For \( x = 12 \): \( 24 , ? , 20 \) → This is true if we use \( > \) or \( \geq \).

To make the inequality true for all three solutions (10, 11, and 12), the only symbol that satisfies this condition is \( \geq \).

Therefore, the correct symbol to use in place of the question mark is \( \geq \):

\[ 2x \geq 20 \]