Which inequality is represented by this graph? + 1 2 3 4 5 6 7 8 9 x > 3 x?3 x>4 x?4
The Correct Answer and Explanation is:
The correct answer is x ≥ 4.
To determine which inequality is represented by the graph, we need to analyze two key features on the number line: the type of circle used at the starting point and the direction of the arrow.
First, let’s examine the starting point of the shaded region. The graph begins at the number 4. The circle at 4 is a closed, or filled-in, circle. In graphing inequalities, a closed circle signifies that the starting number itself is included in the set of possible values. This “inclusive” condition corresponds to the “or equal to” part of an inequality, which is represented by the symbols ≥ (greater than or equal to) or ≤ (less than or equal to). Therefore, we know the inequality will involve the number 4 and an “or equal to” component.
Second, we need to look at the direction of the red line and arrow. The arrow points to the right side of the number line. On a standard number line, values increase as you move to the right. This direction indicates that we are interested in all numbers that are “greater than” the starting point.
By combining these two pieces of information, we can construct the full inequality. The closed circle at 4 means “or equal to 4,” and the arrow pointing to the right means “greater than.” Together, this translates to “greater than or equal to 4.” When we represent this using the variable ‘x’, the inequality is written as x ≥ 4.
Let’s quickly review the other options to confirm our answer:
- x > 4 would be represented by an open circle at 4 with an arrow pointing to the right.
- x ≥ 3 would be represented by a closed circle at 3 with an arrow pointing to the right.
- x > 3 would be represented by an open circle at 3 with an arrow pointing to the right.
Thus, the only option that correctly matches the graph with its closed circle at 4 and an arrow pointing to the right is x ≥ 4.
