Question

А) 4 |х-4|=4Б) 24|6х-10|=-40​

Answer 1

A) 4|x-4|=4

    |x-4|=4/4

    |x-4|=1

    Если что то этот знак =} обозначает больше или равно

   x-4=}0                x-4{0

   x-4=1                 -(x-4)=1

   x=1+4                 -x+4=1

   x=5                    -x=1-4

                               -x=-3

                                x=3

Ответ:x=5,x=3

Б) 24|6x-10|=-40

   |6x-10|=-40/24

   x равен пустому множеству

 Потому что модуль не может быть отрицательным числом

Ответ:x равен пустому множеству

   

Answer 2

Let's solve the equations step by step:

A) 4 |x - 4| = 4

To solve this equation, we need to consider two cases:

Case 1: x - 4 ≥ 0 (i.e., x ≥ 4) In this case, the absolute value |x - 4| is equal to (x - 4). Substituting this into the equation, we get: 4(x - 4) = 4 Now, solve for x: 4x - 16 = 4 4x = 4 + 16 4x = 20 x = 20 / 4 x = 5

Case 2: x - 4 < 0 (i.e., x < 4) In this case, the absolute value |x - 4| is equal to -(x - 4) because it becomes negative. Substituting this into the equation, we get: 4(-(x - 4)) = 4 -4x + 16 = 4 -4x = 4 - 16 -4x = -12 x = -12 / -4 x = 3

So the solutions for the equation 4 |x - 4| = 4 are x = 3 and x = 5.

B) 24 |6x - 10| = -40

This equation involves an absolute value on the left side that results in a negative value on the right side, which is not possible. Therefore, there are no solutions to this equation. Absolute values are always non-negative, so the left side of the equation is non-negative, while the right side is negative.

In summary: A) The solutions for 4 |x - 4| = 4 are x = 3 and x = 5. B) There are no solutions for 24 |6x - 10| = -40.