There is no solution to this equation.
Explanation:
|x| means absolute value of x. Absolute value is the distance a number is from 0 on a number line; since it is distance, it cannot be a negative number.
To solve this equation, |x|+10=1, we would subtract 10 from both sides:
|x|+10-10=1-10; |x|=-9.
This has us looking for a value that would make an absolute value negative; there is no such number.