# Solve the inequality

0.1x³-0.6x²-0.1+20<0
Can we solve without plotting graph

Error in last number
It's 2 not 20
Correct question
0.1x³-0.6x²-0.1x+2 < 0

This one also
|2-1/x| ≤ 2 + |1/x|

Anyone?

#1 multiply by 10
#2 \color{blue} { traingular\ inequality}

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Didn't get abt triangular inequality

The roots of the first equation are not very nice otherwise the idea is to use wavy curve method

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Please explain in detail and solve because i didn't know other method of plotting graph rather than using calculator

• watch after 15 min

We can't apply this here

Why soo we cant apply??
Now search mod inequities in google

If x<0
|2- \frac{1}{x}| \implies 2-\frac{1}{x}=LHS
RHS=2-\frac{1}{x} As \frac{1}{x}<0
If x>0
|2-\frac{1}{x}| \leq 2+ \frac{1}{x}

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Square both sides you'll get
\frac{8}{x} \geq 0

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How to use triangle in equality here

I didn't use triangular inequality here.

No. I want to know how to use triangle inequality here

Take complex numbers 2,\frac{1}{z} and apply
|a-b| \le |a|+|b|