ExplanationYou can Plug In or solve on this problem. To Plug In, choose a value that fits one of the answer choices, such as x = 2, which would fit in the range for choice (C). If x = 2, then \(|-3x + 1| = 5\), which is true, so we can eliminate any answer choice that doesn’t include x = 2: choices (A), (D), and (E).
Logically, it doesn’t make sense that an inequality with a < sign would have a ≤ sign when it’s been solved, but to be sure, check x = −2. In that case, \(|-3x + 1| = 7,\) and is not < 7, so the answer must be choice (B). If you solve this problem, remember that you have to solve both \(-3x + 1 < 7\), and \(-3x + 1 > 7\).
Also remember that you must flip the sign any time you multiply or divide both sides of an inequality by a negative number.
_________________
SandyIf you found this post useful, please let me know by pressing the Kudos ButtonTry our free Online GRE Test