HSPT Question of the Day

1. $x=0$ (correct answer)
2. $x=6$
3. $x=-6$
4. $x=3$

Explanation: When you encounter a linear equation with decimals and parentheses like this one, your goal is to systematically simplify both sides until you isolate the variable. The key is working carefully through the order of operations and decimal arithmetic. Start by distributing $0.25$ to both terms inside the parentheses: $0.25(8x + 12) = 0.25 \cdot 8x + 0.25 \cdot 12 = 2x + 3$. Your equation becomes: $2x + 3 - 3 = 0.5x$, which simplifies to $2x = 0.5x$. Now subtract $0.5x$ from both sides: $2x - 0.5x = 0$, giving you $1.5x = 0$. When any number times $x$ equals zero, then $x = 0$. Let's verify: substituting $x = 0$ into the original equation gives $0.25(0 + 12) - 3 = 3 - 3 = 0$, and $0.5(0) = 0$. Both sides equal zero, confirming our answer. Looking at the wrong choices: Choice B ($x = 6$) likely comes from calculation errors in the distribution step. Choice C ($x = -6$) might result from sign errors when moving terms between sides. Choice D ($x = 3$) could come from confusing the simplified form $2x + 3 - 3$ and thinking the constant term somehow becomes the answer. The correct answer is A. Strategy tip: With decimal coefficients, convert them to fractions if needed ($0.25 = \frac{1}{4}$, $0.5 = \frac{1}{2}$) to avoid arithmetic mistakes, and always verify your solution by substituting back into the original equation.