Q.Solve the compound inequality $-1 \le 2x + 5 < 9$ for $x$ an integer, and list the solution set.

[!TLDR] Operate on all three parts (subtract 5, then divide by the positive number 2), then restrict to int …

Start with $-1 \le 2x + 5 < 9$. Subtract $5$ from all three parts: $-6 \le 2x < 4$. Divide all three parts by the positive number $2$ (no flip): $-3 \le x < 2$. As real numbers the solution is the interval $[-3, 2)$; restricting to integers gives every intege …

Solve the compound inequality for real $x$ first by operating on all three parts, then list only the integers lying …

A common slip is including $x=2$ in the integer list, forgetting the right-hand inequality is strict ($<9$, not $\le 9 …