Help, Im stuck....
I cannot remember what to do.
(x+6)(x-7)(x+4)>0
The solution set is....{x, }
Thank you:)
The function changes sign at x = -6, 7 and -4.
It is positive only where all three terms are positive (x > 7) , or where one factor term is positive and two are negative (-6 < x < -4)
Put that into set terminology.
23 more than t
To solve the inequality (x+6)(x-7)(x+4)>0, we need to find the values of x that make the expression greater than zero.
Here's how we can approach it step by step:
1. Find the critical points: Critical points are the values of x that make any of the factors equal to zero. In this case, we have three critical points: x = -6, x = 7, and x = -4.
2. Plot the critical points on a number line:
-6 -4 7
3. Choose test points: Select any value from each of the intervals created by the critical points to determine if the expression is positive or negative. Some commonly used test points are -10, 0, and 10.
4. Evaluate the expression at the test points:
- For x < -6 (e.g., x = -10), we can choose -10 as a test point.
(-10+6)(-10-7)(-10+4) = (-4)(-17)(-6) = 408 (positive)
- For -6 < x < -4, we can choose 0 as a test point.
(0+6)(0-7)(0+4) = (6)(-7)(4) = -168 (negative)
- For -4 < x < 7, we can also choose 0 as a test point.
(0+6)(0-7)(0+4) = (6)(-7)(4) = -168 (negative)
- For x > 7 (e.g., x = 10), we can choose 10 as a test point.
(10+6)(10-7)(10+4) = (16)(3)(14) = 672 (positive)
5. Analyze the intervals: Look for the intervals where the expression is greater than zero.
- In the interval (-∞, -6), the expression is positive.
- In the interval (-4, 7), the expression is negative.
- In the interval (7, ∞), the expression is positive.
6. Form the solution set: Combine the intervals where the expression is greater than zero.
The solution set is the union of the intervals (-∞, -6) and (7, ∞).
Therefore, the solution set is {x | x < -6 or x > 7}.