Question

what is an alternative way to write the solutions for the compound inequality ( x > - 1 ) and ( x > - 6 )?
( x > - 1 )
( - 1 < x < - 6 )
( x > - 6 )
( - 6 < x < - 1 )

Explanation:

Step1: Analyze the compound inequality

We have \(x > - 1\) and \(x > - 6\). When dealing with “and” in inequalities, the solution must satisfy both conditions.

Step2: Determine the more restrictive inequality

Since \(-1>-6\), if \(x\) is greater than \(-1\), it is automatically greater than \(-6\). So the compound inequality \(x > - 1\) and \(x > - 6\) is equivalent to \(x > - 1\).

Answer:

\(x > - 1\) (i.e., the first option)