Express the given interval as an inequality in terms of x, and select the graph of the interval.
[tex](-8,2)[/tex]
The inequality is $\square$.
Answer (1)
The interval ( − 8 , 2 ) represents all numbers between − 8 and 2 , excluding the endpoints.
This is expressed as the inequality − 8 < x < 2 .
The graph is a number line with open circles at − 8 and 2 , and the region between them shaded.
The inequality representing the interval is − 8 < x < 2 .
Explanation
Understanding the Interval The given interval is ( − 8 , 2 ) . This means that we are considering all real numbers between − 8 and 2 , but not including − 8 and 2 themselves.
Expressing as an Inequality To express this interval as an inequality in terms of x , we write − 8 < x < 2 . This inequality states that x is greater than − 8 and less than 2 .
Visualizing the Interval The graph of this interval would be a number line with open circles at − 8 and 2 , and the region between them shaded.
Examples
Understanding intervals and inequalities is crucial in various fields. For instance, in physics, when describing the possible range of velocities of a particle, or in economics, when defining the range of acceptable prices for a product. In everyday life, you might use intervals to describe the time window you're available for a meeting, like 'between 2 PM and 4 PM'. Expressing these ranges mathematically helps in clear communication and precise calculations.
