Question

Which inequality below represents the one graphed on the number line below?

Number line with open circle at 3 shaded to the right.

Group of answer choices


4x+2>2
3x-2≤7
4x+2≤2
3x-2>7

Answer 1

To determine which inequality corresponds to the number line you described, we need to analyze the characteristics of the graph:

- There is an open circle at 3, which indicates that 3 is not included in the solution.
- The shading is to the right of 3, which means the solution includes all numbers greater than 3.

This means we are looking for an inequality of the form \( x > 3 \) (or another variable that implies the same notion).

Now, let's simplify each of the given inequalities to see which one can lead to the solution \( x > 3 \):

1. **\( 4x + 2 > 2 \)**
Simplifying:
\( 4x > 0 \)
\( x > 0 \)
(This does not match the graph.)

2. **\( 3x - 2 ≤ 7 \)**
Simplifying:
\( 3x ≤ 9 \)
\( x ≤ 3 \)
(This is the opposite of the graph.)

3. **\( 4x + 2 ≤ 2 \)**
Simplifying:
\( 4x ≤ 0 \)
\( x ≤ 0 \)
(This does not match the graph.)

4. **\( 3x - 2 > 7 \)**
Simplifying:
\( 3x > 9 \)
\( x > 3 \)
(This matches the graph.)

Therefore, the inequality that represents the shaded region on the number line (open circle at 3, shaded to the right) is:

**\( 3x - 2 > 7 \)**