|x|-4x=15

To solve the equation \(|x| - 4x = 15\), we need to consider two cases based on the definition of absolute value.

Case 1: \(x \geq 0\)

In this case, \(|x| = x\). So the equation becomes:

\[ x - 4x = 15 \]

This simplifies to:

\[ -3x = 15 \]

Now, divide both sides by -3:

\[ x = -5 \]

Since \(-5\) does not satisfy the condition for this case (\(x \geq 0\)), this solution is not valid.

Case 2: \(x < 0\)

In this case, \(|x| = -x\). So the equation becomes:

\[ -x - 4x = 15 \]

This simplifies to:

\[ -5x = 15 \]

Now, divide both sides by -5:

\[ x = -3 \]

Since \(-3\) is less than \(0\), this solution is valid.

Conclusion

The solution to the equation \(|x| - 4x = 15\) is:

\[ \boxed{-3} \]