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Chapter 2: Problem 6

Write each statement in simplified interval notation. $$ x \geq-5 \text { and } x>2 $$

Short Answer

Expert verified
\((2, \infty)\)

Step by step solution

01

Identify the Intersection

The problem requires expressing the interval where both conditions, \(x \geq -5\) and \(x > 2\), hold true simultaneously. This means we need the intersection of these two conditions.
02

Simplify Each Condition

First, let's express each condition separately. - \(x \geq -5\) is the interval from \(-5\) to infinity, written as \([-5, \infty)\).- \(x > 2\) is the interval from \(2\) to infinity, written as \((2, \infty)\).
03

Find the Intersection of Intervals

The intersection of \([-5, \infty)\) and \((2, \infty)\) is the set of all \(x\) values that satisfy both conditions. This means \(x\) must be greater than \(2\). So the intersection is \((2, \infty)\).
04

Write in Interval Notation

The solution in interval notation representing both \(x \geq -5\) and \(x > 2\) is \((2, \infty)\). This shows the range of \(x\) values that satisfy both inequalities.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Intersection of Intervals
When working with intervals, the intersection refers to the set of numbers that are common to two or more intervals.
For this, it's crucial to identify the point where the conditions overlap and hold true simultaneously.
In the example provided, we have the interval
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