Question

16x²≤8x Памогите плиз

Answer 1

16x² ≤  8x
16x² - 8x ≤  0
Левая часть неравенства -  квадратичная функция. 
Исследуем её на нули и построим схематичный график
16x² - 8x = 0
8x ( 2х - 1 )  = 0
x = 0          или       2х - 1 = 0
                               2х = 1
                                х = 1/2
Расставим знаки функции на числовой прямой ,  учитывая что ветви параболы направлены вверх:

         +              /////////////////////////////////////             +
__________0____________________1/2____________    
                                         -

ОТВЕТ:  [  0  ;    1/2   ].

Answer 2

Solving the Inequality 16x² ≤ 8x

To solve the inequality 16x² ≤ 8x, we can start by rearranging the inequality to set it to zero on one side:

16x² - 8x ≤ 0

Next, we can factor out the common term, 8x, from the left-hand side:

8x(2x - 1) ≤ 0

Now, we have factored the inequality into a product of two expressions. To find the solution, we can use the concept of intervals and test points within those intervals.

Finding the Solution Intervals

We can identify the critical points by setting each factor equal to zero:

1. 8x = 0 => x = 0 2. 2x - 1 = 0 => 2x = 1 => x = 1/2

So, the critical points are x = 0 and x = 1/2.

Testing Intervals

We can test the intervals created by these critical points to determine where the inequality is satisfied.

1. Test the interval to the left of x = 0, for example, x = -1. 2. Test the interval between x = 0 and x = 1/2, for example, x = 1/4. 3. Test the interval to the right of x = 1/2, for example, x = 1.

Determining the Solution

By testing the intervals, we can determine the solution to the inequality 16x² ≤ 8x.

- For x < 0, the expression 8x(2x - 1) is positive, so it does not satisfy the inequality. - For 0 < x < 1/2, the expression 8x(2x - 1) is negative, so it satisfies the inequality. - For x > 1/2, the expression 8x(2x - 1) is positive, so it does not satisfy the inequality.

Conclusion

Therefore, the solution to the inequality 16x² ≤ 8x is:

0 < x ≤ 1/2