A student claims that the inequality \(3x + 1 > 0\) is always true because multiplying a number by 3 and then adding 1 to the result always produces a number greater than 0. Explain the student's error.
Answer (3)
If you multiply 3 by -1 and add 1 it'll be a -2 which is less than zero.
The statement that the inequality 3x+1>0 is always true is incorrect. The solution to the inequality is x > -1/3, and not all real numbers will satisfy this inequality. ;
The inequality 0"> 3 x + 1 > 0 is not always true; it is true only for values of x greater than − 3 1 . The student's error was assuming it holds for all real numbers. For example, if x = − 1 , the left side becomes − 2 , which fails the inequality.
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