Answer to Question #35996 in Algebra for yanny

Question

For what value of x is this inequality |x – 6| < - 8 true? Why?

Answer 1

The absolute value (or modulus) |a| of a real number a is the non-negative value of a.
|a| = a for the positive a, |a| = -a for the negative a. In other words, |a|>=0 for all real a.
That's why inequality |x – 6| < - 8 is not correct for all real x.
There doesn't exist x for which inequality |x – 6| < - 8 is true.