Question

the inequality -x² - 6 < 0 has . done

Explanation:

Step1: Analyze the inequality form

The inequality is \(-x^{2}-6 < 0\). Let's rewrite it as \(x^{2}+ 6>0\) (by multiplying both sides by - 1, and reversing the inequality sign).

Step2: Analyze the expression \(x^{2}+6\)

For any real number \(x\), the square of \(x\) (i.e., \(x^{2}\)) is always non - negative (\(x^{2}\geqslant0\)). Then \(x^{2}+6\) is always greater than or equal to \(6\) (since \(x^{2}\geqslant0\), so \(x^{2}+6\geqslant0 + 6=6\)). And since \(6>0\), \(x^{2}+6>0\) for all real numbers \(x\). So the inequality \(-x^{2}-6 < 0\) (which is equivalent to \(x^{2}+6>0\)) is true for all real numbers \(x\), meaning it has infinitely many solutions (or all real numbers as solutions).

Answer:

infinitely many solutions (or all real numbers as solutions)