Graphical Solution of Absolute Value Inequality |x-2| + |2x+1| ≥ 3

[@reubenmanzo2054]

Personally, I find it easier to solve these sorts of problems algebraically:
|x-2|+|2x+1|>=3
(x-2)^2+2|(x-2)(2x+1)|+(2x+1)^2>=9 (squaring both sides)
5x^2+5+2|2x^2-3x-2|>=9
|2x^2-3x-2|>=(4-5x^2)/2
(2x^2-3x-2)^2>=(4-5x^2)^2/4 (squaring both sides again, to fully remove the absolute values)
4x^4-12x^3+x^2+12x+4>=(25x^4-40x^2+16)/4
16x^4-48x^3+4x^2+48x+16>=25x^4-40x^2+16
9x^4+48x^3-44x^2-48x

[@gybx4094]

Interesting approach. I like it.

[@fa18sd43]

Awesome! Thanks a bunch. This helps me help my high school son.

[@nickyraja3793]

Saved my day, absolutely ingenious!

[@johnchang1226]

What is cases?

[@izachelton470]

Wow! Loved it.

[@aishahkadir3257]

its really help me a lot,,,,,thanksss

[@karabomashabane8461]

Good Day
what would happen if the one absolute value was subtracting the other?
Your response would be highly appreciated.

[@drancosavale2010]

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[@asafharpaz7514]

this is really great

[@pranjalverma3501]

thank you very much sir

[@MatthewCaspi]

👍🏼

[@Tracks777]

Excellent video

[@kshitizz7052]

I once dreamt to be taught by such teacher.
My school techers are just Bookish fellow ,ruining life.🤮🤮

[@shak8941]

Omg you're amazing

[@mitralalmitralal6871]

(-6)×(-4)

[@DeepakKumar-eg3ul]

confusion in this

[@boomza12130]

Thx XD

[@benpenner5974]

bri"ish!

[@dhritimondal7292]

This graph is a bit wrong. The lines y=2-x and y=-1-2x won't intersect because they are parallel to each other.