Question

(x+3)(x-5)<0 vhhhhjjjcxcghcvh​

Answer 1

Пошаговое объяснение:

(x+5)(x-3) < 0

(x+5)(x-3) = 0

x+5=0

x-3=0

x=5

x=3

Ответ: xЄ (-5;3)

Answer 2

To solve the inequality $(x+3)(x-5) < 0$, we can use the method of sign analysis or interval notation. We need to find the intervals for which the expression is negative.

1. Find the critical points by setting each factor equal to zero:

   • $x+3 = 0$ gives $x = -3$
   • $x-5 = 0$ gives $x = 5$

2. Now we have three intervals to consider: $(-\infty, -3)$, $(-3, 5)$, and $(5, \infty)$.

3. Test a point from each interval in the original inequality to determine the sign of the expression within that interval:

   • Pick a number less than -3, e.g., -4: $(-4+3)(-4-5) = (-1)(-9) = 9 > 0$
   • Pick a number between -3 and 5, e.g., 0: $(0+3)(0-5) = (3)(-5) = -15 < 0$
   • Pick a number greater than 5, e.g., 6: $(6+3)(6-5) = (9)(1) = 9 > 0$

4. Based on the sign analysis, we see that the expression is negative in the interval $(-3, 5)$.

Therefore, the solution to the inequality $(x+3)(x-5) < 0$ is $x$ belongs to the open interval $(-3, 5)$. In interval notation, this can be represented as $(-3, 5)$.