Absolute value, the way of solving

Question

$$0>1,4 -\mid2,6-x\mid$$ Have i done it in good way ?? $$-\mid2,6-x\mid<-1,4$$ $$(-\mid2,6-x\mid<-1,4)*(-1)$$ $$\mid2,6-x\mid>1,4$$

Now we've got 2 possibilities $$2,6-x>1,4$$ and $$2,6-x>-1,4$$

THE RESULTS: $$x < 1,2$$ $$x < 4$$

Answer 1

Your one fault is that the your second "possibility" is wrong.

It should be

$$2.6-x < -1.4$$

An easy way to think about it is that you need the LHS to be "more" negative than $-1.4$, because that will make its absolute value bigger than $1.4$

When working with multiplying/dividing negatives as well as working with absolute values, you're gonna need to grow comfortable with switching the inequality sign and knowing when to do so.

Final answer should be

$$x < 1.2$$ $$x > 4$$

Answer 2

$$|2.6-x|>1.4$$ is

$$2.6-x>1.4\text{ or }x-2.6>1.4$$

which is

$$x<1.2\text{ or }x>4.$$