SOLUTION: If a and b are negative and c is positive, which of the following must be true?
i) c - (a + b) > 0 ii) (a - c)(b - c) > 0 iii) (a - b)(c - b) > 0
a) (i) and (ii) only
b) (i
Algebra.Com
Question 284722: If a and b are negative and c is positive, which of the following must be true?
i) c - (a + b) > 0 ii) (a - c)(b - c) > 0 iii) (a - b)(c - b) > 0
a) (i) and (ii) only
b) (i) and (iii) only
c) (ii) and (iii) only
d) (i), (ii), and (iii)
e) none of these
Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
i) c - (a + b) > 0
(positive) - (negative) > 0
This is always positive.
ii) (a - c)(b - c) > 0
ab - bc - ac + c^2 > 0
(positive) - (negative) - (negative) + (positive) > 0
This depends on the values of a, b, and c.
iii) (a - b)(c - b) > 0
ac - bc - ab + b^2 > 0
(negative) - (negative) - (positive) + (positive) > 0
This depends on a, b, and c.
RELATED QUESTIONS
If x is a negative number, which of the following must be true?
I) x^5 < |x|
II) x <... (answered by Edwin McCravy,Theo)
If x is a negative number, which of the following must be true?
I) x^5 < |x|
II) x <... (answered by CubeyThePenguin)
If X, Y are non-zero integers and X/Y < |X/Y| < Y, which of the following must be true?
(answered by greenestamps)
If (x^2)(y^3)z < 0, which of the following statements must be true?
I. yz < 0
II. xz... (answered by richard1234)
Which of the following are true for all integers a,b, and c?
I.(a+b)+c=a+(b+c)... (answered by josgarithmetic,ikleyn,math_tutor2020)
the graph of ax+by=5 in the xy-plane contains points from each of quadrants I,II and III, (answered by Boreal,solver91311)
If x(x - y) = 0 and x > y, which of the following statements must be true?
I. x =... (answered by jim_thompson5910)
If m(p + r) = 0, then which of the following expressions must be true?
I. m = 0 II. (answered by Fombitz)
If xy>0 and xz<0, which of the following statements must be true?
I. x+y+z>0
II.... (answered by ikleyn)