Question 1150767: I was taking a practice test and got the following question wrong:
Solve the following inequality:
-12x -3 > 45
1. x = -8
2. x = -5.3
3. x = -4
4. x = -3.5
The correct answer is "x = -8." However, I selected number 2 (x = -5.3).
Both answers, when multiplied by -12 is greater than 45. Why is #2 wrong?
Found 3 solutions by MathLover1, MathTherapy, ikleyn:
Answer by MathLover1(20849)   (Show Source):
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website! I was taking a practice test and got the following question wrong:
Solve the following inequality:
-12x -3 > 45
1. x = -8
2. x = -5.3
3. x = -4
4. x = -3.5
The correct answer is "x = -8." However, I selected number 2 (x = -5.3).
Both answers, when multiplied by -12 is greater than 45. Why is #2 wrong?
I'm sure you did solve and see that x < - 4, so that makes both x = - 5.3 and x = - 8, correct. You must've left something out because the difference between
the 2 answers is that one is an INTEGER and the other is not. There must be other info that you failed to include that'll make - 8 the answer as opposed to - 5.3.
OR
The question may be to determine the SMALLEST value that'll make the inequality TRUE. In this case, it'll be - 8. AGAIN, I believe important details/instructions have not been presented!
Answer by ikleyn(52778)  (Show Source):
You can put this solution on YOUR website! .
In Math, the words "Solve the following inequality" mean "Find all solutions of the following inequality".
These two combinations of words are synonyms : each is equivalent to the other.
When after these words and after the given inequality the list of particular values follows, it is NOT a solution to the problem.
It means that this problem, as it is worded, printed and presented in your post, is assigned, as the test,
by the person UNFAMILIAR with the standard usage of words and terms in Math.
In more simple expressions, the formulation of this problem, as presented in the post, is INCORRECT.
The solution to this problem is the set of all real numbers x such that x < -4.
And the number -8, as well as the number -5.3, are particular solutions to the problem, but not the entire solution "in whole".
If the person, who formulated the problem, wanted to ask "which of the numbers from the following list satisfies to the given inequality ?",
then he (or she) must formulate the question/(the problem) correspondingly.
In any case, the options 1) and 2) of the post BOTH SATISFY to the given inequality, as it is presented in the post.
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