Question

What is the solution set for the exponential inequality? (–[infinity], 2) (2, [infinity]) (–2, 2) (–[infinity], 2) ∪ (2, [infinity])

Answer 1

The solution set for the exponential inequality is
`\( (-\infty, 2) \cup (2, \infty) \).`

Step-by-step explanation:

The given exponential inequality is represented by two intervals:
`\( (-\infty, 2) \) and \( (2, \infty) \)`. This indicates that the solution set includes all real numbers less than 2 and all real numbers greater than 2 but excludes the value 2 itself. The union of these two intervals forms the complete solution set.

In mathematical notation, this can be expressed as
`\( (-\infty, 2) \cup (2, \infty) \)`. The open intervals exclude the boundary values, and the union symbol (\cup) denotes the combination of both intervals. This solution set encompasses all real numbers except for 2.

It's crucial to understand that exponential inequalities involve the exponentiation of a variable, and the solution set depends on the specified conditions. In this case, the solution set reflects the regions where the inequality holds true, ensuring a comprehensive understanding of the permissible values for the given inequality.