Solve the inequality $-3x + 5 \le 17$ for $x$.

Subtract 5 from both sides: $-3x \le 12$. Divide both sides by $-3$. Because we are dividing by a **negative** number, the inequality direction **reverses**: $x \ge -4$. The solution set is all numbers greater than or equal to $-4$. - Trap A keeps the same direction and the same sign — the most common error. - Trap B forgets the sign on $-4$. - Trap D both reverses the inequality (correct) and drops the sign (incorrect). Load-bearing rule: multiplying or dividing both sides of an inequality by a **negative** number flips $<$ to $>$ (and $\le$ to $\ge$). Addition/subtraction never flips.