Question

196. 1) |×+1|+2=-83) 3|x-1|=1/3+1 2/3​

Answer 1

Ответ:

1) |х+1|+2=-8

|х+1|=-8-2

хє- немає розв'язку

3) 3|х-1|=1/3+1 1 2/3

3|х-1|=1/3+5/3

3|х-1|=2

|х-1|=-2/3

х=5/3

х=1/3

х1=1/3; х2=5/3

Answer 2

To solve the equation |x + 1| + 2 = 3|x - 1| = 1/3 + 1 2/3, you can follow these steps:

1. First, simplify the right side of the equation, 1/3 + 1 2/3, to get a single fraction:

   1/3 + 1 2/3 = 1/3 + (1 + 2/3) = 1/3 + 3/3 = 4/3

2. Now, you have the equation |x + 1| + 2 = 3|x - 1| = 4/3.

3. Since you have two absolute value expressions equal to a constant, you will need to split this into two separate cases and solve for each case.

   Case 1: x + 1 is positive or zero, and x - 1 is positive or zero.

   For x + 1 ≥ 0 and x - 1 ≥ 0: x + 1 + 2 = 3(x - 1) + 4/3

   Simplify: x + 3 = 3x - 3 + 4/3

   Combine like terms: x + 3 = 3x - 9/3 + 4/3

   x + 3 = 3x - 5/3

   Move x terms to one side and constants to the other: 2x = -3 - 5/3

   2x = -14/3

   x = (-14/3) / 2

   x = -7/3

   Case 2: x + 1 is negative, and x - 1 is negative.

   For x + 1 < 0 and x - 1 < 0: -(x + 1) + 2 = -3(x - 1) + 4/3

   Simplify: -x - 1 + 2 = -3x + 3 + 4/3

   Combine like terms: -x + 1 = -3x + 9/3 + 4/3

   -x + 1 = -3x + 13/3

   Move x terms to one side and constants to the other: 2x = 13/3 - 1

   2x = 13/3 - 3/3

   2x = 10/3

   x = (10/3) / 2

   x = 5/3

So, the solutions to the equation are x = -7/3 and x = 5/3.