Question

Mr. Edmonds gave his students an inequality and told them to write possible solutions.

3x + 2(4x + 2) less than 2(6x + 1)



What values would be incorrect student responses? Select TWO correct answers.

Group of answer choices

0

4

2

3

Answer 1

Let's first solve the inequality to find the possible values for \(x\).

Starting from the inequality:

\[ 3x + 2(4x + 2) < 2(6x + 1) \]

First, expand both sides:

\[ 3x + 8x + 4 < 12x + 2 \]

Combine like terms on the left side:

\[ 11x + 4 < 12x + 2 \]

Now, isolate \(x\):

Subtract \(11x\) from both sides:

\[ 4 < x + 2 \]

Then, subtract \(2\) from both sides:

\[ 2 < x \]

This simplifies to:

\[ x > 2 \]

Now, this means any value of \(x\) that is greater than 2 is a correct solution to the inequality. Values less than or equal to 2 would be incorrect solutions.

Among the given options:

- **0** (incorrect, since \(0 < 2\))
- **4** (correct, since \(4 > 2\))
- **2** (incorrect, since \(2 < 2\) is not true)
- **3** (correct, since \(3 > 2\))

Thus, the two incorrect student responses are:

- **0**
- **2**