Can anyone please help with this inequality,(x+20)(x-10)(x+11)>0
The solution set is {x| }
The distinct roots of the equation
f(x) = (x+20)(x-10)(x+11) = 0
are x=-20, x=10 and x=-11
Therefore the graph changes sign three times.
When x-> -∞, f(x)<0
When x-> ∞, f(x)>0
Therefore
f(x) > 0 when
x=(10,∞) and
x=(-20,-11)
Graph the function to verify the solution.
OK what you say make sense but I am unsure of the solution sets of {x| }
x=(10,∞) and
x=(-20,-11)
represent the two intervals on which x>0.
The solution set is the union of the two intervals.
If you need help with the interval notation, you can try:
http://zonalandeducation.com/mmts/miscellaneousMath/intervalNotation/intervalNotation.html
To solve the inequality (x+20)(x-10)(x+11) > 0, we need to find the values of x that satisfy this inequality.
First, let's find the critical points where the expression (x+20)(x-10)(x+11) changes sign.
Set each factor equal to zero and solve for x:
x+20 = 0 => x = -20
x-10 = 0 => x = 10
x+11 = 0 => x = -11
These values of x divide the number line into four intervals:
(-∞, -20), (-20, -11), (-11, 10), (10, ∞).
Now, we need to determine the sign of the expression (x+20)(x-10)(x+11) in each of these intervals.
Choose a test point from each interval and plug it into the expression to see if it's positive or negative:
In the interval (-∞, -20), let's choose x = -30:
(-30+20)(-30-10)(-30+11) = (-10)(-40)(-19) = 760, which is positive.
In the interval (-20, -11), let's choose x = -15:
(-15+20)(-15-10)(-15+11) = (5)(-25)(-4) = 500, which is negative.
In the interval (-11, 10), let's choose x = 0:
(0+20)(0-10)(0+11) = (20)(-10)(11) = -2200, which is negative.
In the interval (10, ∞), let's choose x = 15:
(15+20)(15-10)(15+11) = (35)(5)(26) = 4550, which is positive.
From these test points, we can determine the sign of the expression in each interval:
(-∞, -20): positive
(-20, -11): negative
(-11, 10): negative
(10, ∞): positive
The inequality states that the expression (x+20)(x-10)(x+11) is greater than zero. Therefore, we are looking for the intervals where the expression is positive.
The solution set can be represented as:
{x | x < -20 or -11 < x < 10}