SOLUTION: a) Write an inequality that results in “no solution.” b) Solve your inequality. c) Explain why the answer is “no solution.”

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Question 1160569: a) Write an inequality that results in “no solution.”
b) Solve your inequality.
c) Explain why the answer is “no solution.”

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Inequalities with no solution:
What you're looking for in the case of inequalities with no solution is nonsense. Yes, that's right: you are looking for nonsense. If you come across an inequality that indicates information that is not true, then the inequality has no solution.
Let's look at a few examples.
-> nonsense (no solutions exist)
Why? Absolute values can't be less than or equal to numbers.
Simplify this inequality. Is there a solution or not?
No. The simplified inequality is nonsense.

-> nonsense (no solutions exist)

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

            The statement in the post by @MathLover1, that the absence of solutions
            of inequality means  NONSENSE  is    w r o n g   and   i n c o r r e c t. 


There are thousands examples from real life and from Math, when absence of solutions is absolutely normal and regular situation.


For example, consider inequality

    sin(x) > 1.


It has no solutions; but the sinusoid exists and there is no any NONSENSE in it . . . 



Another example.  Let y be the position in time of the ferries cabine (y is the height over the ground).

The inequality y < 0 has no solutions, and it is very good.

It only means that the the ferry is designed correctly (!)

Would the inequality y < 0 had solutions, it would mean death or injury of people in cabin.



Another widely known inequality is  x^2 < 0.

It has no solutions (the square of the real number CAN NOT be negative), and it is absolutely normal situation.


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