0.1x³-0.6x²-0.1+20<0

Can we solve without plotting graph

# Solve the inequality

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}

Didn't get abt triangular inequality

Please solve both

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

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

Please solve both

Why soo we cant apply??

Now search mod inequities in google

Can you please upload solution

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}

Square both sides you'll get

\frac{8}{x} \geq 0

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|