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

Предыдущий
вопрос Следующий
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 - 2
(2x+1)(2x-1) = 4x^2 - 2x + 2x - 1 = 4x^2 - 1

So the original inequality becomes:

5x^2 - 3x - 2 - (4x^2 - 1) < 27
5x^2 - 3x - 2 - 4x^2 + 1 < 27
x^2 - 3x - 1 < 27
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.