Problem: Find the number of roots of the equation 3 ∣x∣ −∣2−∣x∣∣=1.

Solution:
There are different methods to solve this equation but one simple method is as follows:

Step 1: Simplify the given equation
3 ∣x∣ −∣2−∣x∣∣=1
Since the absolute value of a number is always non-negative, we can split the equation into two cases:
Case 1: x ≥ 0
3x −(2−x) = 1
Simplifying this equation, we get:
4x = 3
x = 3/4
Case 2: x < />
3(−x) −(2−(−x)) = 1
Simplifying this equation, we get:
−4x = −3
x = 3/4
Notice that the solution in both cases is the same. This means that the equation has only one root.

Step 2: Check if the root satisfies the equation
We found that x = 3/4 is the only root of the equation. Let's check if it satisfies the equation:
3 ∣3/4∣ −∣2−∣3/4∣∣=1
3 (3/4) −(2−3/4) = 9/4 − 5/4 = 1
The left-hand side of the equation is equal to the right-hand side, so the root is valid.

Step 3: Write the final answer
The equation 3 ∣x∣ −∣2−∣x∣∣=1 has only one root, which is x = 3/4.