Question

6. решите уравнение: 1) [x] = 6; 2) 7/x| = 35; 3) |x| - 9 = 15. пж срочно​

Answer 1

Ответ:

1. x1=-6 x2=6
2. x1=-5 x2=5
3. x1=-24 x2=24

Answer 2

1. = 6:

The equation [x] = 6 represents the greatest integer less than or equal to x equals 6. Since 6 is an integer, the value of x must lie between 6 and 7. Therefore, the solution to this equation is x ∈ [6, 7).

2. 7/x| = 35:

The equation 7/x| = 35 implies that the absolute value of 7 divided by x is equal to 35. We can solve this equation by considering two cases: one when x is positive and another when x is negative.

Case 1: x > 0 In this case, the equation becomes 7/x = 35. By cross-multiplication, we have 7 = 35x, which gives x = 7/35 = 1/5.

Case 2: x < 0 In this case, the equation becomes 7/(-x) = 35. Again, by cross-multiplication, we have 7 = -35x. Dividing both sides by -35, we get x = 7/-35 = -1/5.

So, the solutions to the equation are x = 1/5 and x = -1/5.

3. |x| - 9 = 15:

To solve this equation, we can isolate the absolute value term and consider two cases: one when x is positive and another when x is negative.

Case 1: x > 0 In this case, |x| = x. Substituting this into the equation, we have x - 9 = 15. Adding 9 to both sides gives x = 15 + 9 = 24.

Case 2: x < 0 In this case, |x| = -x. Substituting this into the equation, we have -x - 9 = 15. Adding 9 to both sides and multiplying by -1, we get x = -15 - 9 = -24.

Therefore, the solutions to the equation are x = 24 and x = -24.