Question

6) (x + 5)(x + x + 6) > 0;​

Answer 1

Ответ:

Объяснение:

(x + 5)(x + x + 6) > 0

(x+5)(2x+6)>0

x+5=0      ;  2x+6=0

x=-5            2x=-6

                     x2=-3

x∈(-∞;-5) U(-3;+∞)

Answer 2

To solve the inequality $(x + 5)(x + x + 6) > 0$, you can follow these steps:

1. Factorize the expression: $(x + 5)(x + x + 6) = (x + 5)(2x + 6)$

2. Simplify further: $(x + 5)(2x + 6) = 2(x + 5)(x + 3)$

3. Identify critical points: Set each factor equal to zero and solve for $x$:

   • $x + 5 = 0 \Rightarrow x = -5$
   • $x + 3 = 0 \Rightarrow x = -3$

4. Create intervals: Use the critical points to create intervals on the number line: $(- \infty, -5), (-5, -3), (-3, \infty)$.

5. Test each interval: Choose a test point from each interval and plug it into the factored expression. Determine the sign of the expression in each interval.

   • For $x < -5$, choose $x = -6$: $2(-6 + 5)(-6 + 3) = 2(-1)(-3) = 6 > 0$
   • For $-5 < x < -3$, choose $x = -4$: $2(-4 + 5)(-4 + 3) = 2(1)(-1) = -2 < 0$
   • For $x > -3$, choose $x = 0$: $2(0 + 5)(0 + 3) = 2(5)(3) = 30 > 0$

6. Determine the solution:

   • The solution is $-\infty < x < -5$ or $x > -3$.

Therefore, the solution to the inequality $(x + 5)(x + x + 6) > 0$ is $-\infty < x < -5$ or $x > -3$.