Question

Solve the equation. \(|x+8|-2=-12\)

Short answer

The equation \( |x+8|-2=-12 \) has no real solutions because the absolute value of a number minus 2 cannot result in a negative number.

Step-by-step solution

Analyze the structure of the problem

Observe that the problem given is an absolute value equation and the form on the right side of the equation that is \( |x+8|-2=-12 \) is less than zero. But the absolute value of a number is always non-negative, meaning this equation does not have a solution.

Confirm the answer

To confirm, we can note that any value for 'x' substituted into \( |x+8|-2 \) will yield a non-negative result. Subtracting 2 from a non-negative number will not result in -12, meaning this equation has no real solutions.