Write the inequality using interval notation. Graph the inequality.
X≥13
Answer (2)
Express the inequality X ≥ 13 in interval notation.
The interval notation is [ 13 , ∞ ) .
Graph the inequality on a number line with a closed circle at 13 and shading to the right.
The solution extends to positive infinity. The final answer is [ 13 , ∞ ) .
Explanation
Understanding the Inequality The given inequality is X ≥ 13 . We need to express this inequality in interval notation and describe how to graph it.
Expressing in Interval Notation In interval notation, X ≥ 13 means that X can be any value from 13 (inclusive) to positive infinity. We use a square bracket to indicate that 13 is included in the interval and the infinity symbol ∞ to represent positive infinity.
The Interval Notation Therefore, the interval notation for X ≥ 13 is [ 13 , ∞ ) .
Graphing the Inequality To graph this inequality, we draw a number line. We place a closed circle (or a square bracket) at 13 on the number line to indicate that 13 is included in the solution. Then, we shade the region to the right of 13, indicating that all values greater than 13 are also part of the solution. Finally, we draw an arrow at the end of the shaded region to indicate that the solution extends to positive infinity.
Examples
Imagine you are measuring the height of students in a class, and you only want to consider students who are at least 130 cm tall. The inequality X ≥ 130 represents this situation, where X is the height of a student. In interval notation, this would be [ 130 , ∞ ) , meaning you are considering all heights from 130 cm upwards. Graphing this on a number line helps visualize the range of heights you are interested in.
The inequality X ≥ 13 is expressed in interval notation as [ 13 , ∞ ) . To graph it, we use a closed circle at 13 and shade to the right, indicating all values equal to or greater than 13. The solution extends infinitely to the right, covering all values above 13.
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