Question

(x-14)(x+10)<0решение подскажит6​

Answer 1

Ответ:

Пошаговое объяснение:

Сначала решим уравнение

(Х-14)(х+10)=0

1) х-14=0; х=14

2) х+10=0 ; х=-10

Нанесем корни на числовую прямую

-------------(-10)-----------14-----------

Получится три интервала

Определим знак выражения (х-14)(х+10) на каждом интервале. Для этого берем из каждого интервала любое число и подставляем вместо х в выражение

Х= 15; (15-14)(15+10)=25>0

Х=0; (-14)×10=-140<0

Х=-15; (-15-14)(-15+10)=-24(-5)=120>0

Выбираем интервалы на которых выражение больше 0

Х=(- бесконечность;-10) U(14;+бесконечность)

Answer 2

To solve this inequality, we need to find the values of x that make the expression (x-14)(x+10) less than zero.

We can use the following steps to solve the inequality:

Step 1: Find the critical points The critical points are the values of x that make the expression equal to zero. In this case, we have: (x - 14)(x + 10) = 0 x = 14 or x = -10

Step 2: Create a number line We can create a number line and mark the critical points on it:

---------------------o----------------------o--------------------- -10 14

Step 3: Test each interval We can choose a test value from each interval and substitute it into the expression to determine whether it is positive or negative. If it is negative, then all values in that interval will satisfy the inequality.

For example, if we choose x = -11 (a value less than -10), then we get: (-11 - 14)(-11 + 10) = (-25)(-1) = 25 > 0

This means that the expression is positive when x is less than -10.

If we choose x = 0 (a value between -10 and 14), then we get: (0 - 14)(0 + 10) = (-14)(10) = -140 < 0

This means that the expression is negative when x is between -10 and 14.

If we choose x = 15 (a value greater than 14), then we get: (15 - 14)(15 + 10) = (1)(25) = 25 > 0

This means that the expression is positive when x is greater than 14.

Step 4: Write the solution From the above analysis, we can see that the expression (x-14)(x+10) is negative for values of x between -10 and 14. Therefore, the solution to the inequality is: -10 < x < 14

In interval notation, the solution is: (-10, 14)