Question

Помоги плиз* Розв’яжіть нерівність х2-7х-30<0

Answer 1

х²-7х-30<0

x²-10x+3x-30<0

x(x-10)+3(x-10)<0

(x+3)(x-10)<0

x∈(-3,10)

Answer 2

I can help you solve the inequality x^2 - 7x - 30 < 0. Here are the steps:

1. Factor the quadratic expression x^2 - 7x - 30 as (x - 10)(x + 3). 2. Find the values of x that make the expression zero: x = 10 or x = -3. These are the critical points that divide the number line into three intervals: (-∞, -3), (-3, 10), and (10, ∞). 3. Test each interval to see if the expression is negative or positive. You can use any value in the interval, but it is easier to use the midpoint. For example, in the interval (-∞, -3), you can use x = -4. Plug this value into the expression and see if it is negative or positive. Repeat this for the other two intervals. 4. The expression is negative when x is in the interval (-3, 10). This is the solution set of the inequality. You can write it as -3 < x < 10 or using interval notation as (-3, 10).

Here is a graph of the expression and the solution set:

![graph](#graphic_art(prompt="a graph of x^2 - 7x - 30 < 0 with the solution set shaded