Tachs Math Question of the Day

1. $x \ge \dfrac{13}{3}$ (correct answer)
2. $x \le \dfrac{13}{3}$
3. $x \ge 3$
4. $x \le 3$

Explanation: When you encounter an inequality with fractions, your goal is to isolate the variable while preserving the inequality's direction. The key principle is that you can perform the same operations on both sides of an inequality as you would with an equation, as long as you don't multiply or divide by a negative number. Starting with $\dfrac{3x - 5}{4} \ge 2$, first multiply both sides by 4 to eliminate the fraction: $3x - 5 \ge 8$. Next, add 5 to both sides: $3x \ge 13$. Finally, divide both sides by 3: $x \ge \dfrac{13}{3}$. Since we only multiplied and divided by positive numbers, the inequality sign stays the same. Looking at the wrong answers: Choice B gives $x \le \dfrac{13}{3}$, which flips the inequality sign incorrectly—this would happen if you mistakenly thought you needed to reverse the sign when dividing by a positive number. Choice C gives $x \ge 3$, which results from incorrectly adding 5 to the right side instead of adding it (getting $3x \ge 3$). Choice D combines both errors: the wrong constant and the flipped inequality sign. The key strategy for inequality problems is to treat them exactly like equations until you multiply or divide by a negative number—only then do you flip the inequality sign. Also, always double-check your arithmetic when combining fractions and whole numbers, as it's easy to make calculation errors under test pressure.