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

Question

Substitute in 10, 11 and 12 individually.

Ex 2(10) = ?, then 2(11) = ?, then 2(12) = ?.

Then pick the inequality sign that makes all three statements true

(1 point)
Responses

<
<

>
>

≤
≤

≥

Answer 1

To find the appropriate symbol to replace the question mark in the inequality \(2x , ? , 20\), we will evaluate the left side of the inequality for the values 10, 11, and 12, and then see what inequality holds true for each calculation.

1. Substitute \(x = 10\): \[ 2(10) = 20 \] Thus, we have \(20 , ? , 20\).

2. Substitute \(x = 11\): \[ 2(11) = 22 \] Thus, we have \(22 , ? , 20\).

3. Substitute \(x = 12\): \[ 2(12) = 24 \] Thus, we have \(24 , ? , 20\).

Now, we summarize the results:

• For \(x = 10\): \(20 , ? , 20\) (this holds true with \(\leq\) or \(=\)).
• For \(x = 11\): \(22 , ? , 20\) (this holds true with \(>\)).
• For \(x = 12\): \(24 , ? , 20\) (this holds true with \(>\)).

Now we evaluate possible inequality signs:

• \(<\): Not true for \(x = 10\) (20 is not less than 20).
• \(>\): Not true for \(x = 10\) (20 is not greater than 20).
• \(\leq\): True for \(x = 10\) (20 is equal to 20), and true for \(x = 11\) and \(x = 12\).
• \(\geq\): True for \(x = 10\), \(11\), \(12\) (both \(22\) and \(24\) are greater than 20).

The only inequality that holds true for all values (10, 11, and 12) is:

Answer: \(\geq\)