If a+b is negative, which statement must be true ?

Question

(a)a < 0, b<0

(b) a<0

(c) a<0, b> 0

(d) a<-b

i think I understand the question and my answer might be a but I'm not sure how to show my work 

 

Answer 1

Negative means less than 0 so the statement given is a+b < 0

Subtracting b from both sides gives a+b-b < 0-b which simplifies to a < -b which is choice (d)

Answer 2

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Two numbers, a and b, are added together and the sum is negative (less than zero). So ONE or BOTH NUMBERS must be negative. If a is negative, b can be either positive or negative. But maybe a is positive, and b negative? What if they are BOTH negative? Knowing this, which choice ALWAYS works? a

Answer 3

Lets try each case.

 

choice A states that you add two negatives.  Adding two negative gives you a negative sum.

 

-2 + (-2) = -4

 

 

choice B states that a is negative.  This can have flexibility because it means that b can be either positive or negative and has no restrictions.

 

-2 + (-3) = -5    ----> negative

 

-2 + 3 = 1  ------> positive

 

 

choice C states that a is positive and b is negative.

 

-2 + 3 = 1           sum is positive

 

 

choice D states that a is less than the negative value of b.

 

-5 + (-3) = -8         negative

 

-10 + (-6) = -16     negative

 

 

Just as Roman mentioned, choice D works, but so does choice A.