What is x^3-2x^2<x^2(x-2)-3(x-1) ?

The solution to x^3-2x^2<x^2(x-2)-3(x-1) is x<1

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x^3-2x^2<x^2(x-2)-3(x-1)

x^{3} - 2 x^{2} < x^{2} (x - 2) - 3 (x - 1)

x < 1

Interval Notation

(- \infty, 1)

Solution steps

x^{3} - 2 x^{2} < x^{2} (x - 2) - 3 (x - 1)

Rewrite in standard form

x - 1 < 0

Move

1

to the right side

x < 1

- x^{3} + 13 x - 12

x^{2} - 13 x + 36 = 0

(x^{2} + 2 x)^{2} - 2 (x^{2} + 2 x) - 3

2 (h - 6) + 20 = - 4

3 x^{2} - 8 x

What is x^3-2x^2<x^2(x-2)-3(x-1) ?
The solution to x^3-2x^2<x^2(x-2)-3(x-1) is x<1