Question

what is an alternative way to write the solutions for the compound inequality $x>5$ or $x\geq8$? $8 < x < 5$ $5 < x < 8$ $x\geq8$ $x>5$

Explanation:

Step1: Analyze the compound inequality

The compound inequality \(x > 5\) or \(x\geq8\) means that \(x\) can take any value greater than \(5\). Because if \(x\) is greater than \(8\), it is also greater than \(5\).

Step2: Check each option

• Option \(8 < x < 5\): This is impossible since \(8>5\), no number can satisfy this.
• Option \(5 < x < 8\): This only represents a part of the solutions of \(x > 5\) (excluding \(x\geq8\) and some values of \(x>5\) like \(x = 6\) is included but \(x=9\) is not in this interval).
• Option \(x\geq8\): This only represents a part of the solutions of \(x > 5\) (missing values like \(x = 6\)).
• Option \(x>5\): If \(x>5\), it includes all values that satisfy \(x > 5\) (when \(x>5\), if \(x\geq8\) it is still part of \(x > 5\) because \(x\geq8\Rightarrow x>5\) (since \(8>5\))).

Answer:

\(x > 5\)