Algebra practice question

Answer: A. −2 < x ≤ 3

Apply each step to all three parts. Subtract 3: −4 < 2x ≤ 6. Divide by 2: −2 < x ≤ 3. The inequality symbols stay as they were because 2 is positive.

Why the other answers are wrong

B. −2 ≤ x < 3

The strict and non-strict symbols are swapped. The original has < on the left and ≤ on the right, and those don't change.

C. 1 < x ≤ 6

The 3 was added instead of subtracted: −1 + 3 = 2 and 9 + 3 = 12, halved to 1 and 6. Undoing '+3' means subtracting 3.

D. −4 < x ≤ 12

The 3 was subtracted but the division by 2 was skipped: −4 < 2x ≤ 12 isn't finished until both ends are halved.

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