Tachs Math Question of the Day

1. $-5$
2. $13$
3. $\dfrac{7}{2}$
4. $5$ (correct answer)

Explanation: This question tests your ability to substitute values into algebraic expressions and follow the order of operations correctly. When you're given that $x = 6$, you need to substitute this value into the expression $\frac{3x}{2} - 4$ and calculate step by step. First, substitute: $\frac{3(6)}{2} - 4$. Next, multiply in the numerator: $\frac{18}{2} - 4$. Then divide: $9 - 4$. Finally, subtract: $5$. Let's examine why each wrong answer appears. Choice A ($-5$) likely comes from making a sign error somewhere in the calculation, perhaps treating the subtraction incorrectly or making an arithmetic mistake that flips the sign. Choice B ($13$) suggests you might have added 4 instead of subtracting it, getting $9 + 4 = 13$. Choice C ($\frac{7}{2}$) indicates you probably subtracted 4 from the numerator before dividing: $\frac{18-4}{2} = \frac{14}{2} = 7$, then mistakenly left it as $\frac{7}{2}$ instead of converting to the whole number 7. This violates the order of operations since you must complete the division $\frac{18}{2}$ before subtracting 4. The key strategy here is to always follow the order of operations (PEMDAS) carefully. When substituting values into expressions, work methodically through each step and double-check your arithmetic. Watch especially for the common trap of performing operations in the wrong sequence when fractions are involved.