Thank you for answering (x+20)(x -10)(x+11)>0. How do I write the solution set of {x| }
To write the solution set of {x| }, we need to determine the values of x that satisfy the given inequality (x+20)(x -10)(x+11) > 0.
To do this, we can use the concept of interval notation. Here's how you can find the solution set:
Step 1: Determine the critical values
The critical values are the points where the expression inside the inequality changes sign. In this case, the critical values are the values of x that make the factors equal to zero. So, we 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
Step 2: Create intervals
Now, we will divide the number line into intervals using the critical values.
-∞---(-20)---(-11)---(10)---∞
Step 3: Test a value in each interval
Choose a test point in each interval and evaluate the expression (x+20)(x -10)(x+11) using the test point. If the result is greater than zero, then all values in that interval satisfy the inequality. If the result is less than zero, then all values in that interval do not satisfy the inequality.
Test in the interval (-∞, -20):
Let's choose x = -21 (a value smaller than -20).
(-21 + 20)(-21 -10)(-21+11) = (-1)(-31)(-10) = -310 > 0
Test in the interval (-20, -11):
Let's choose x = -15 (a value between -20 and -11).
(-15 + 20)(-15 -10)(-15+11) = (5)(-25)(-4) = 500 < 0
Test in the interval (-11, 10):
Let's choose x = 0 (a value between -11 and 10).
(0 + 20)(0 - 10)(0 + 11) = (20)(-10)(11) = -2200 < 0
Test in the interval (10, ∞):
Let's choose x = 15 (a value greater than 10).
(15 + 20)(15 - 10)(15 + 11) = (35)(5)(26) = 18200 > 0
Step 4: Write the solution set
Based on the test results, we can conclude that the solution set is:
{x | -∞ < x < -20 or -11 < x < 10}