What is the correct first step when solving 2(3x − 1) + 4 = 18?
ASubtract 4 from both sides.
BDivide both sides by 2.
CDistribute 2 to get 6x − 2 + 4 = 18.
DAdd 1 to both sides.
The first phase is always to simplify each side. Parentheses must be cleared by distributing before you can combine like terms or use inverse operations. Subtracting 4 or dividing by 2 first would leave the parentheses unresolved and produce incorrect results.
Question 2 True / False
When distributing −3 across (x − 5), the correct result is −3x − 15.
TTrue
FFalse
Answer: False
Distributing means multiplying −3 by each term inside: −3 · x = −3x and −3 · (−5) = +15. A negative times a negative is positive, so the result is −3x + 15. Writing −3x − 15 is one of the most common algebra errors and stems from only applying the sign to the first term or forgetting the sign rule for multiplication.
Question 3 Short Answer
After solving a multi-step equation and finding x = 4, why should you substitute 4 back into the original equation rather than a simplified version?
Think about your answer, then reveal below.
Model answer: Substituting into the original equation checks every step of your work, including any distributing or combining done during simplification. A simplified version may already contain an error, so checking against it would not catch that mistake.
Each simplification step is an opportunity for an arithmetic or sign error. The original equation is the ground truth — if your answer satisfies it, the solution is correct regardless of what happened in between. Checking a simplified form only validates the final inverse-operation steps, not the earlier simplification steps.