The equation you provided is an absolute value equation:

$|1 - 5x| = 16$

To solve for $x$, we must consider the two possible cases for the absolute value expression, since the absolute value of a number represents its distance from zero, meaning it could be either positive or negative.

Case 1: $1 - 5x = 16$

Solve this equation normally: $1 - 5x = 16$ Subtract 1 from both sides: $-5x = 16 - 1$ $-5x = 15$ Now, divide both sides by $-5$: $x = \frac{15}{-5} = -3$

Case 2: $1 - 5x = -16$

Solve this equation similarly: $1 - 5x = -16$ Subtract 1 from both sides: $-5x = -16 - 1$ $-5x = -17$ Now, divide both sides by $-5$: $x = \frac{-17}{-5} = \frac{17}{5}$

Final solution:

The two possible solutions are: $x = -3 \quad \text{or} \quad x = \frac{17}{5}$

Do you want any further details or have any questions?

Here are 5 related questions:

1. How would you solve $|2x - 3| = 7$?
2. What happens if there is no solution in an absolute value equation?
3. Can an absolute value equation have more than two solutions?
4. How does the graph of an absolute value function look?
5. What is the definition of an absolute value inequality?

Tip: Always check the solutions of an absolute value equation by substituting them back into the original equation to ensure correctness.