Question

(2х-6)•(5+х)меньше 0

Answer 1

2x-6×5+x=0

2x+x=30

3x=30

x=10

Answer 2

To solve the inequality expression, let's first expand the brackets:

(2x - 6) * (5 + x) < 0

Expanding the brackets, we get:

10x + 2x^2 - 30 - 6x < 0

Combining like terms, we have:

2x^2 + 4x - 30 < 0

Now, let's find the solutions to the quadratic equation:

2x^2 + 4x - 30 = 0

We can factorize this quadratic equation:

2(x^2 + 2x - 15) = 0

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

Setting each factor to zero:

x + 5 = 0 or x - 3 = 0

Solving for x, we find:

x = -5 or x = 3

Now we have three critical points on the number line: -5, 3, and 0.

We can now test the inequality in each interval:

For x < -5: Choose x = -6: (2(-6) - 6) * (5 + (-6)) = (-12 - 6) * (-1) = (-18) * (-1) = 18 > 0

For -5 < x < 0: Choose x = -1: (2(-1) - 6) * (5 + (-1)) = (-2 - 6) * (4) = (-8) * (4) = -32 < 0

For 0 < x < 3: Choose x = 1: (2(1) - 6) * (5 + 1) = (-4) * (6) = -24 < 0

For x > 3: Choose x = 4: (2(4) - 6) * (5 + 4) = (8 - 6) * (9) = (2) * (9) = 18 > 0

From the above analysis, we can see that the inequality (2x - 6) * (5 + x) < 0 holds true for -5 < x < 0.

Therefore, the solution to the inequality is -5 < x < 0.