(5x+2)(x-1)-(2x+1)(2x-1)<27

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вопрос

To solve this inequality, we first need to expand the expressions on both sides:

(5x+2)(x-1) = 5x^2 - 5x + 2x - 2 = 5x^2 - 3x -
(2x+1)(2x-1) = 4x^2 - 2x + 2x - 1 = 4x^2 - 1

So the original inequality becomes:

5x^2 - 3x - 2 - (4x^2 - 1) < 2
5x^2 - 3x - 2 - 4x^2 + 1 < 2
x^2 - 3x - 1 < 2
x^2 - 3x - 28 < 0

Now we need to factor the quadratic expression to solve for x:

(x - 7)(x + 4) < 0

The solutions to this inequality are x < -4 and x > 7. Therefore, the solution to the original inequality is -4 < x < 7.