Question

Решите неравенство: 1. x^2-6х-7<02. -9х-143. -7х30

Answer 1

Объяснение:

рисунок..............

Answer 2

1. x^2 - 6x - 7 < 0:

To solve this inequality, we can find the critical points by setting the expression equal to zero:

x^2 - 6x - 7 = 0

Factoring the quadratic equation, we have:

(x - 7)(x + 1) = 0

Setting each factor equal to zero:

x - 7 = 0 -> x = 7 x + 1 = 0 -> x = -1

Now, we have three intervals to test: (-∞, -1), (-1, 7), and (7, +∞).

Choosing a test point from each interval and substituting it into the original inequality:

Let's use x = -2 (from (-∞, -1)): (-2)^2 - 6(-2) - 7 = 4 + 12 - 7 = 9 > 0

Let's use x = 0 (from (-1, 7)): 0^2 - 6(0) - 7 = -7 < 0

Let's use x = 8 (from (7, +∞)): 8^2 - 6(8) - 7 = 64 - 48 - 7 = 9 > 0

From the test points, we can see that the inequality is satisfied for x values in the interval (-1, 7). Therefore, the solution to the inequality x^2 - 6x - 7 < 0 is:

-1 < x < 7

2. -9x - 14 < 3:

To solve this inequality, we can isolate the variable x:

-9x - 14 < 3 -9x < 3 + 14 -9x < 17

To remove the negative coefficient, we multiply both sides of the inequality by -1, and remember to flip the inequality sign:

-1 * (-9x) > -1 * 17 9x > -17

Dividing both sides of the inequality by 9, remembering to flip the inequality sign again:

x < -17/9

The solution to the inequality -9x - 14 < 3 is x < -17/9.

3. -7x + 3 < 0:

To solve this inequality, we can isolate the variable x:

-7x + 3 < 0

Subtracting 3 from both sides of the inequality:

-7x < -3

Dividing both sides of the inequality by -7 and flipping the inequality sign:

x > 3/7

The solution to the inequality -7x + 3 < 0 is x > 3/7.