I posted this before but could not understand the answer. How do I write the solution set of:
{x| } for (x+20)(x -10)(x+11)>0
Would someone please verify my answer for the solution set of (x+20)(x -10)(x+11)>0, {x|(-20,-11)<x<(10, �‡)}
Would someone please verify my answer for the solution set of (x+20)(x -10)(x+11)>0, {x|(-20,-11)<x<(10,infinity sign)}
To find the solution set of the inequality (x+20)(x-10)(x+11) > 0, we can follow a step-by-step process:
Step 1: Identify the critical points:
To solve the inequality, we need to determine the values of x that make the expression (x+20)(x-10)(x+11) equal to zero. These values are known as the critical points:
-20 (from x + 20 = 0),
10 (from x - 10 = 0),
-11 (from x + 11 = 0).
Step 2: Determine the intervals:
Next, we need to divide the number line into intervals based on the critical points. We have four intervals: (-∞, -20), (-20, -11), (-11, 10), (10, ∞).
Step 3: Test the intervals:
Now, we will pick a test value from each interval and substitute it into the inequality. We can choose easy numbers like -30, -15, 0, and 15.
For interval (-∞, -20):
Let's test x = -30:
(-30 + 20)(-30 - 10)(-30 + 11) = (-10)(-40)(-19) = -7,600
Since -7,600 is less than zero, the inequality is not satisfied.
For interval (-20, -11):
Let's test x = -15:
(-15 + 20)(-15 - 10)(-15 + 11) = (5)(-25)(-4) = 2,000
Since 2,000 is greater than zero, the inequality is satisfied.
For interval (-11, 10):
Let's test x = 0:
(0 + 20)(0 - 10)(0 + 11) = (20)(-10)(11) = -2,200
Since -2,200 is less than zero, the inequality is not satisfied.
For interval (10, ∞):
Let's test x = 15:
(15 + 20)(15 - 10)(15 + 11) = (35)(5)(26) = 45,500
Since 45,500 is greater than zero, the inequality is satisfied.
Step 4: Determine the solution set:
Based on our tests, we can conclude that the values of x that make the inequality (x+20)(x-10)(x+11) > 0 true are in the intervals (-20, -11) and (10, ∞).
Therefore, the solution set can be written as:
{x | -20 < x < -11 or x > 10}