AlgebraEasy–MediumInequality with a negative coefficient
Algebra practice question
Which of the following describes all values of x for which 5 − 2x > 11?
- A. x < −3Correct
- B. x > −3
- C. x < 3
- D. x > 8
Answer: A. x < −3
Subtract 5: −2x > 6. Divide by −2 and REVERSE the inequality: x < −3. Check with x = −4: 5 + 8 = 13 > 11.
Why the other answers are wrong
- B. x > −3
- Dividing by a negative number reverses the inequality sign. x > −3 fails: at x = 0, 5 > 11 is false.
- C. x < 3
- x < 3 loses the sign of −3. At x = 0, 5 − 0 = 5, which isn't greater than 11.
- D. x > 8
- x > 8 comes from moving 5 the wrong way (11 − 5 = 6 was needed, not 11 + 5), and at x = 9 the expression is −13.
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