Solve: 3(x - 2) ≥ 9

Question

Solve: 3(x - 2) ≥ 9

Accepted Answer

x ≥ 5. Starting with 3(x - 2) ≥ 9, divide both sides by 3: x - 2 ≥ 3. (Since we divided by a positive number, the inequality direction stays the same.) Add 2 to both sides: x ≥ 5. Alternatively, distribute first: 3x - 6 ≥ 9, then 3x ≥ 15, then x ≥ 5.

The solution x ≥ 3 results from forgetting to add 2 after dividing by 3, stopping at x - 2 ≥ 3 and incorrectly reading the 3 as the answer. The solution x ≥ 1 might come from subtracting 2 instead of adding it in the last step, computing 3 - 2 = 1. The solution x ≤ 5 incorrectly reverses the inequality sign; since we only divided by a positive number and added a positive number, the inequality direction should not change.

Solving linear inequalities is a fundamental skill for the DSST exam. Students should solve inequalities using the same algebraic steps as equations, with the critical exception that multiplying or dividing by a negative number reverses the inequality. This problem uses only positive operations, so the direction remains unchanged.

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