Question

what is an alternative way to write the solutions for the compound inequality $x < 10$ or $x leq -5$?
$10 < x leq -5$
$-5 leq x < 10$
$x leq -5$
$x < 10$

Explanation:

Step1: Analyze option A

For \(10 < x\leq - 5\), since \(10>-5\), there is no number \(x\) that satisfies this inequality.

Step2: Analyze option B

\(-5\leq x < 10\) represents the intersection of \(x < 10\) and \(x\geq - 5\), not the union (or) of \(x < 10\) and \(x\leq - 5\).

Step3: Analyze option C

\(x\leq - 5\) only represents one part of the compound inequality \(x < 10\) or \(x\leq - 5\).

Step4: Analyze option D

The compound inequality \(x < 10\) or \(x\leq - 5\) means all real numbers less than \(10\). Because if \(x\leq - 5\), it is already included in \(x < 10\) (since \(-5<10\)).

Answer:

D. \(x < 10\)