Joaquin and Serena are looking at the problem \(3x + 1 > 0\).

Serena says that the inequality is always true because multiplying a number by three and then adding one to it makes the number greater than zero. Is she right? Explain why or why not.

Unfortunately, Serena is not correct. She has apparently lost sight of most of the world of negative numbers.
In fact, if 'x' is ANY number less than negative 1/3, then 3x+1 is less than zero.
There are a huge load of numbers that qualify.

Answered by AL2006 | 2024-06-10

Serena is wrong. She has completely ignored negative numbers. With negative numbers, it is possible to have an answer that is less than zero. For example, x=-2 3(-2)+1= -5 which is not > than 0.

Answered by hannah2019290 | 2024-06-10

Serena is incorrect because the inequality 0"> 3 x + 1 > 0 is not universally true. It is only true for values of x greater than − 3 1 ​ . Examples like x = − 1 or x = − 2 1 ​ show that the inequality does not hold for all values.
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Answered by AL2006 | 2024-10-11