Question

Решить неравенство (2x-5)(x+5)/7-x решить

Answer 1

Ответ:

-2x + 5 ≤ -3x - 3

-2х + 3х ≤ -3 - 5

х ≤ - 8

   

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                       -8

(-∞; - 8]

ОТВЕТ:  (-∞; - 8]

Пошаговое объяснение:

Answer 2

To solve the inequality:

(2x-5)(x+5)/(7-x) > 0

We need to first find the critical values of x, which are the values of x that make the expression in the numerator or the denominator equal to zero.

So, we have:

2x-5 = 0 -> x = 2.5

x+5 = 0 -> x = -5

7-x = 0 -> x = 7

Now, we can divide the number line into four intervals based on these critical values:

Interval 1: x < -5 Interval 2: -5 < x < 2.5 Interval 3: 2.5 < x < 7 Interval 4: x > 7

We can then test a point in each interval to determine the sign of the expression in the numerator:

Interval 1: Let x = -6 (2x-5)(x+5)/(7-x) = (-17)(-1)/(-13) = 17/13 > 0

Interval 2: Let x = 0 (2x-5)(x+5)/(7-x) = (-5)(5)/(7) = -25/7 < 0

Interval 3: Let x = 5 (2x-5)(x+5)/(7-x) = (5)(10)/(2) = 25 > 0

Interval 4: Let x = 8 (2x-5)(x+5)/(7-x) = (11)(13)/(-1) = -143 < 0

So, the solution to the inequality is:

x < -5 or 2.5 < x < 7

We can express this solution set using interval notation as:

(-infinity, -5) U (2.5, 7)