Question

(х-4)(х+9)>(х+12)(х-7)

Answer 1

X^2+9x-4x-36>x^2-7x+12x-84
x^2+5x-36>x^2+5x-84
x^2+5x-36-x^2-5x+84>0
48>0
Т.е. неравенство верно. Доказано.

Answer 2

To solve the inequality $(x-4)(x+9) > (x+12)(x-7)$, we need to find the values of $x$ that satisfy this inequality. Let's start by expanding both sides of the inequality:

$(x-4)(x+9) > (x+12)(x-7)$

Expanding:

$x^2 + 5x - 36 > x^2 + 5x - 84$

Now, we can simplify the inequality by canceling out the common terms on both sides:

$x^2 + 5x - 36 - (x^2 + 5x - 84) > 0$

Simplify further:

$x^2 + 5x - 36 - x^2 - 5x + 84 > 0$

Combine like terms:

$-36 + 84 > 0$

$48 > 0$

Since $48$ is greater than zero, this means that the inequality is true for all values of $x$. In other words, any real value of $x$ will satisfy the inequality $(x-4)(x+9) > (x+12)(x-7)$.