Inequalities Solutions - wrong answer?

[nycgirl212]

Book: Equations, Inequalities, & VICs
Version: 4.0
p.103: Answer to question 1 is A, but I think it should be C. I checked the errdata page and didn't see this mentioned.

The question is: If 4x-12 ≥ x+9, which of the following must be true?

The simplified equation is x≥7.

Choice C says x>7, so x can be 7.00001, 7.4, 500, etc... all those values satisfy the x≥7, so why is C not the answer? And if the answer is A, could you please provide an explanation. I am confused.

[atharshiraz]

Book: Equations, Inequalities, & VICs
Version: 4.0
p.103: Answer to question 1 is A, but I think it should be C. I checked the errdata page and didn't see this mentioned.

The question is: If 4x-12 ≥ x+9, which of the following must be true?

The simplified equation is x≥7.

Choice C says x>7, so x can be 7.00001, 7.4, 500, etc... all those values satisfy the x≥7, so why is C not the answer? And if the answer is A, could you please provide an explanation. I am confused.

As you said x can be equal to 7 OR x can be greater than 7.
So x=7 OR x>7.

Choice C says that x>7 . This means that x is anything greater than 7 but it is NOT equal to 7.

Choice C does not cover the scenario where x is equal to 7.

The only other choice which covers both scenarios (x=7 or x>7) is choice A which is x>6 which says that x is greater than 6 but it is NOT equal to 6. Choice A is the only one that covers both scenarios where x=7 and x >7.

[nycgirl212]

Book: Equations, Inequalities, & VICs
Version: 4.0
p.103: Answer to question 1 is A, but I think it should be C. I checked the errdata page and didn't see this mentioned.

The question is: If 4x-12 ≥ x+9, which of the following must be true?

The simplified equation is x≥7.

Choice C says x>7, so x can be 7.00001, 7.4, 500, etc... all those values satisfy the x≥7, so why is C not the answer? And if the answer is A, could you please provide an explanation. I am confused.

As you said x can be equal to 7 OR x can be greater than 7.
So x=7 OR x>7.

Choice C says that x>7 . This means that x is anything greater than 7 but it is NOT equal to 7.

Choice C does not cover the scenario where x is equal to 7.

The only other choice which covers both scenarios (x=7 or x>7) is choice A which is x>6 which says that x is greater than 6 but it is NOT equal to 6. Choice A is the only one that covers both scenarios where x=7 and x >7.

The question asks, what MUST BE TRUE.

If we pick choice A, which is x>6, and pick x = 6.5, that does not satisfy the equation of x≥7, because 6.5 is not greater than or equal to 7. That is what is confusing me.

[tim]

you're interpreting the MUST backwards. let me give you an example: i tell you that school X charges an application fee of at least 7 dollars (this is the >=7 part that you correctly deduced). what do you know FOR SURE?

do you know FOR SURE that the fee is more than 7 dollars? no, because it could be exactly 7 dollars, which is not more than 7.

do you know FOR SURE that the fee is more than 6 dollars? of course, because no matter what valid number you choose i am 100% sure it will be more than 6.

note that a correct approach involves picking numbers that satisfy the given inequality and asking which of the answer choices is ALWAYS true. your initial approach did this the other way around.

[nycgirl212]

you're interpreting the MUST backwards. let me give you an example: i tell you that school X charges an application fee of at least 7 dollars (this is the >=7 part that you correctly deduced). what do you know FOR SURE?

do you know FOR SURE that the fee is more than 7 dollars? no, because it could be exactly 7 dollars, which is not more than 7.

do you know FOR SURE that the fee is more than 6 dollars? of course, because no matter what valid number you choose i am 100% sure it will be more than 6.

note that a correct approach involves picking numbers that satisfy the given inequality and asking which of the answer choices is ALWAYS true. your initial approach did this the other way around.

makes sense.. thank you.. the explanation helps

[jnelson0612]

Great! Glad that Tim could help. :-)