For what values of x is |x|-3 = 0 ?utkarshakash said:Homework Statement
Find the solution set of [itex] \large \frac{|x-1|(x-3)(x-5)^{2010}}{(|x|-3)(|x|+1)} \geq 0[/itex]
Homework Equations
I am required to solve this using Wavy-Curve method
The Attempt at a Solution
The critical points are 3 and 5. But I don't know what to do with expressions involving modulus signs.
Not sure how you're defining critical points, but interesting things will happen at -3, 1, 3 and 5. I would break it into the five ranges those points generate and consider each separately.utkarshakash said:The critical points are 3 and 5. But I don't know what to do with expressions involving modulus signs.
SammyS said:For what values of x is |x|-3 = 0 ?
For what values of x is |x|+1 = 0 ?
An inequality involving modulus is an expression that contains a modulus symbol (| |) and compares two quantities by stating that one is greater than or less than the other, while taking into consideration the absolute value of each quantity.
To solve an inequality involving modulus, you must first isolate the absolute value expression on one side of the inequality. Then, you must create two separate inequalities, one with the positive value of the absolute value expression and one with the negative value. Solve each inequality separately and combine the solutions to find the final solution set.
Yes, an inequality involving modulus can have more than one solution. This is because the absolute value of a number can be positive or negative, so when solving the two separate inequalities, you may end up with two different solution sets which can be combined to form the final solution set.
If the modulus is on both sides of the inequality, you will need to remove the modulus on both sides by creating two separate inequalities, one with the positive value of the absolute value expression and one with the negative value. Solve each inequality separately and combine the solutions to find the final solution set.
To graph an inequality involving modulus, you can first graph the corresponding absolute value equation. Then, depending on the inequality symbol, you can shade the region above or below the graph to represent the solutions. If the inequality involves a strict inequality (>, <), the graph should be shaded with a dashed line to indicate that the boundary is not included in the solution set.