AlgebraHardSolving an inequality with distribution on one side
Algebra practice question
Which of the following describes all solutions of 2(x + 3) > 4x − 2?
- A. x < 4Correct
- B. x > 4
- C. x < −4
- D. x > 2
Answer: A. x < 4
2x + 6 > 4x − 2, so 8 > 2x and x < 4.
Why the other answers are wrong
- B. x > 4
- x > 4 reverses the direction; check x = 5: 16 > 18 is false.
- C. x < −4
- x < −4 mishandles the constants (6 + 2 = 8, not −8).
- D. x > 2
- x > 2 comes from 2x + 3 > 4x − 2 (forgetting to distribute the 2 to the 3).
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