Mathematics

The key is recognizing that when you divide or multiply an inequality by a negative number, the inequality sign flips. Since $x < -4$ is already solved for $x$, you need to manipulate $kx > 8$ to match it exactly—which means $k$ must be negative. Work backwards: if $kx > 8$ should give $x < -4$, divide both sides by $k$ and use the sign-flip rule to find what $k$ must be.

The key is recognizing that when you divide or multiply an inequality by a negative number, the inequality sign flips. Since $x < -4$ is already solved for $x$, you need to manipulate $kx > 8$ to match it exactly—which means $k$ must be negative. Work backwards: if $kx > 8$ should give $x < -4$, divide both sides by $k$ and use the sign-flip rule to find what $k$ must be.