$$0>1,4 -\mid2,6-x\mid$$ 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: $$x < 1,2$$ $$x < 4$$
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Sometimes it helps to read the expression form out loud. $|2.6-x|>1.4$ reads: "The distance from $x$ to $2.6$ is greater then $1.4$." – Michael Hoppe Apr 30 '21 at 16:54
2 Answers
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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
$$x < 1.2$$ $$x > 4$$
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1This website does a good job of explaining absolute value inequalities. – matthewleonardson Apr 30 '21 at 14:19
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1Even though the OP did it, you should not leave the final answer without a logical connector. – Apr 30 '21 at 14:28
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$$|2.6-x|>1.4$$ is
$$2.6-x>1.4\text{ or }x-2.6>1.4$$
which is
$$x<1.2\text{ or }x>4.$$