solve the following inequality
x^2(8+x)(x-5)/(x+5)(x-2)>/=0
please show work
Good grief Mya, I answered this one for you and you even replied to it.
Why are you posting it again?
http://www.jiskha.com/display.cgi?id=1346891496
To solve the given inequality, we can start by finding the critical points of the equation, where the expression inside the inequality becomes zero or undefined.
First, we set the numerator equal to zero:
x^2(8+x)(x-5) = 0
This equation will be satisfied when either x^2 = 0, (8+x) = 0, or (x-5) = 0.
These conditions can be written as:
x = 0,
x = -8, and
x = 5.
Now, let's find the values that make the denominator equal to zero:
(x+5)(x-2) = 0
This equation is satisfied when either (x+5) = 0 or (x-2) = 0.
These conditions can be written as:
x = -5,
x = 2.
Now, we have all the critical points:
x = -8, -5, 0, 2, and 5.
To determine the sign of the expression in each interval, we can use test values or create a sign chart.
Let's choose test values for each interval:
-9, -6, 1, 3, and 6.
Now, we calculate the sign of the expression for each test value:
For x = -9:
(-9)^2(8+(-9))(-9-5)(-9-2) = 84120
Since this is positive, it satisfies the inequality.
For x = -6:
(-6)^2(8+(-6))(-6-5)(-6-2) = 11664
Since this is positive, it satisfies the inequality.
For x = 1:
(1)^2(8+1)(1-5)(1-2) = -63
Since this is negative, it does not satisfy the inequality.
For x = 3:
(3)^2(8+3)(3-5)(3-2) = 36
Since this is positive, it satisfies the inequality.
For x = 6:
(6)^2(8+6)(6-5)(6-2) = 6048
Since this is positive, it satisfies the inequality.
Based on the sign chart, the solution to the inequality is:
(-∞, -8] U (-5, -2) U [0, 2) U (5, ∞).