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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-> 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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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)
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.
