Q.Solve $10 - 4x > 2$ for real $x$, being careful with the sign when dividing.

[!TLDR] Isolate the $x$-term, then divide by the negative coefficient $-4$, flipping the inequality. [ …

Start with $10 - 4x > 2$. Subtract $10$ from both sides (Rule 1, no flip): $-4x > -8$. Divide both sides by $-4$, a negative number — by Rule 3 the inequality reverses from $>$ to $<$: $x < 2$. Check $x=0$: $10-4(0)=10>2$ ✓; check the boundary $x=2$: $10- …

Subtract 10 from both sides, then divide by the negative coefficient $-4$, remembe …

Forgetting to flip the sign when dividing by $-4$ would wrongly give $x > 2$ — the single m …