Explanation

You 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.
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When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

Given: |-3x + 1| < 7
In this case, we'll apply Rule #1 to get: -7 < -3x + 1 < 7
Subtract 1 from all 3 sides to get: -8 < -3x < 6
Divide all 3 sides by -3 to get: 8/3 > x > -2 [we REVERSE the inequalities when we divide by a NEGATIVE value]
Rewrite as -2 < x < 8/3

Answer:

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