Question

1064.2) |x -6-29|<84) |3 - x| < 2;6) |15 – x| < 17.​

Answer 1

Ответ:

Пошаговое объяснение:

Решение смотри на фото.

Answer 2

It seems like you have a set of absolute value inequalities involving the variable "x." Let's solve each of these inequalities step by step:

1. |x - 6 - 29| < 84

   First, simplify the expression inside the absolute value:

   |x - 35| < 84

   Now, you can split this inequality into two cases:

   Case 1: x - 35 < 84 x < 84 + 35 x < 119

   Case 2: -(x - 35) < 84 (Note the negative sign on the left side) -x + 35 < 84 -x < 84 - 35 -x < 49

   To isolate x in both cases, multiply both sides by -1 in Case 2 (remember to reverse the inequality sign):

   Case 2 (continued): x > -49

   So, the solution to the first inequality is -49 < x < 119.

2. |3 - x| < 2

   Simplify the expression inside the absolute value:

   |3 - x| < 2

   Now, split it into two cases:

   Case 1: 3 - x < 2 -x < 2 - 3 -x < -1

   To isolate x, multiply both sides by -1 (and reverse the inequality sign):

   Case 1 (continued): x > 1

   Case 2: -(3 - x) < 2 (Note the negative sign on the left side) -3 + x < 2 x < 2 + 3 x < 5

   So, the solution to the second inequality is 1 < x < 5.

3. |15 - x| < 17

   Simplify the expression inside the absolute value:

   |15 - x| < 17

   Split it into two cases:

   Case 1: 15 - x < 17 -x < 17 - 15 -x < 2

   To isolate x, multiply both sides by -1 (and reverse the inequality sign):

   Case 1 (continued): x > -2

   Case 2: -(15 - x) < 17 (Note the negative sign on the left side) -15 + x < 17 x < 17 + 15 x < 32

   So, the solution to the third inequality is -2 < x < 32.

In summary, the solutions to the three given inequalities are as follows:

1. -49 < x < 119
2. 1 < x < 5
3. -2 < x < 32