Solve the absolute value equation |-x| = 3.4.

Step-by-step solution

1. 1

   Simplify the bars with a symmetry identity. For every real $x$, the numbers $x$ and $-x$ sit the same distance from the origin, so

   $|-x|=|x|$

   The equation therefore becomes the much plainer $|x|=3.4$.

2. 2

   Split into two cases. Since $3.4>0$, the value inside the bars can be either sign:

   $x=3.4\qquad\text{or}\qquad x=-3.4$

3. 3

   Do not try to 'cancel' the minus sign instead. A common error is to write $-x=3.4$ and stop, giving only $x=-3.4$. That drops half the solution set: the bars must be removed with a case split, not by treating $-x$ as if it were already positive.

4. 4

   Check both values. $|-(3.4)|=|-3.4|=3.4$ $\checkmark$ and $|-(-3.4)|=|3.4|=3.4$ $\checkmark$. Both work, so the solution set is $\{-3.4,\,3.4\}$.