Final answer:
To solve the equation |4x-1|=2x+9, consider two cases: positive and negative values of 4x-1. Solve each case separately and check for extraneous solutions.
Step-by-step explanation:
To solve the equation |4x-1|=2x+9, we need to consider two cases: when 4x-1 is positive and when it is negative.
When 4x-1 is positive, we have 4x-1=2x+9. Solving for x, we get x=5.
When 4x-1 is negative, we have -(4x-1)=2x+9. Solving for x, we get x=-1.5.
Checking both solutions in the original equation, we find that x=5 is a valid solution, whereas x=-1.5 is an extraneous solution.