How many of the integers that satisfy the inequality (x+2)(x+3)/(x-2)greater than or equal to 0 are less than 5.
a)1 b)2 c)3 d)4 e)5
a)1 b)2 c)3 d)4 e)5
The given expression changes its sign at x = -2, x = -3, and x = 2.quantskillsgmat wrote:How many of the integers that satisfy the inequality (x+2)(x+3)/(x-2)greater than or equal to 0 are less than 5.
a)1 b)2 c)3 d)4 e)5
Now, for values of x which are less than -3, the expression is always negative as all three terms of the expression are individually negative.
Let us check the sign of the expression for integer values of x which are greater than or equal to -3 but less than 5.
For x = -3, (x + 2)*(x + 3)/(x - 2) = 0 ---------------> YES
For x = -2, (x + 2)*(x + 3)/(x - 2) = 0 ---------------> YES
For x = -1, (x + 2)*(x + 3)/(x - 2) = -2/3
For x = 0, (x + 2)*(x + 3)/(x - 2) = -3
For x = 1, (x + 2)*(x + 3)/(x - 2) = -12
For x = 2, (x + 2)*(x + 3)/(x - 2) = Undefined
For x = 3, (x + 2)*(x + 3)/(x - 2) = 30 ---------------> YES
For x = 4, (x + 2)*(x + 3)/(x - 2) = 21 ---------------> YES
Hence, 4 such integers.
The correct answer is D.
