agl89 said:Homework Statement
Solve the inequality for x, given that (4x - 16) / [(x - 3)(x - 9)] < 0
Homework Equations
I can't think of any for this type of problem...
The Attempt at a Solution
(4x - 16) / [(x - 3)(x - 9)] < 0
4(x - 4) / [(x - 3)(x - 9)] < 0
I'm not sure where to go from here. I haven't worked one of these types of problems in awhile...
The first step in solving this inequality is to simplify the expression by multiplying both sides by the common denominator (x - 3)(x - 9).
The inequality sign flips when multiplying both sides by a negative number. This is because multiplying by a negative number on both sides of an inequality switches the order of the numbers, making the smaller number larger and the larger number smaller.
The critical values for this inequality are the values of x that make the denominator equal to zero. In this case, the critical values are x = 3 and x = 9. These values must be excluded from the solution set.
Yes, you can use a calculator to solve this inequality. However, be sure to double check your solution by plugging it back into the original inequality to ensure it is true.
Yes, there can be more than one possible solution to this inequality. The solution set will depend on the value of x and the given inequality. It is important to check if any critical values are included or excluded in the solution set.