If |x + 1|

Question

If |x + 1| <= 5 and |y - 1| <= 5, what is the least possible value of the product xy ?

A. -36
B. -24
C. -16
D. 8
E. 0

Mansoor50 · Answer

solving for x and y we get:

x=(4,-6)
y=(6,-4)

the least value is -36

Archit3110 · Answer

solve for |x + 1| <= 5 and |y - 1| <= 5

we get x= -6,4 and y= -4,6

least value would be =36 IMO A

T1101 · Answer

A "trick" I once saw used by Bunuel in such question involving absolute value and inequalities is to write the inequalities in the following way to get the range quicker and easier: |x + 1| <= 5 --> -5<=x+1<=5 --> -6<=x<=4 |y - 1| <= 5 --> -5<=y-1<=5 --> -4<=y<=6

apoorvishnoi · Answer

We can rewrite the inequalities as following :

|x + 1 | ≤ 5

-5 ≤ x+1 ≤ 5 or -6≤ x ≤ 4 ( Subtracting 1 from the equation )

|y - 1 | ≤ 5

-5 ≤ y-1 ≤ 5 or -4 ≤ y ≤ 6 ( Adding 1 to the equation )

So know we have

-6≤ x ≤ 4 and -4 ≤ y ≤ 6

Now we need to find the “least value” of xy. If we Multiply -6*6 we get -36, which is the least value for xy.

MathRevolution · Answer

|x + 1| ≤ 5 : |x -(-1)| ≤ 5

=> x ≤ 5 - 1 = 4 and x ≤ -5 - 1 = -6

|y - 1| ≤ 5

y ≤ 5 + 1 = 6 and y ≤ -5 + 1 = -4

Least possible value of xy when both are of different sign:

=> x = -6 and y = 6 then xy = -36  
  => x = 4 and y = -4 then xy = -16

Answer A

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If |x + 1| <= 5 and |y - 1| <= 5, what is the least possible value of

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