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Solve the equation. Check for extraneous solutions.
∣4x−1∣=2x+9

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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.

User Ricardo Fercher
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