Question

|x-6 2/9|<8|3-x|《2|15-x|<17​

Answer 1

Ответ:

Пошаговое объяснение:

Решение дано на фото.

Answer 2

To solve the compound inequality involving absolute values:

| x - 6 2/9 | < 8 and 2 | 15 - x | < 17

Let's break it down into two separate inequalities:

1. | x - 6 2/9 | < 8

First, isolate the absolute value expression:

x - 6 2/9 < 8 and x - 6 2/9 > -8

Now, add 6 2/9 to both sides of both inequalities:

x < 8 + 6 2/9 and x > -8 + 6 2/9

Simplify:

x < 62/9 and x > -62/9

So, the first inequality is:

-62/9 < x < 62/9

2. 2 | 15 - x | < 17

Divide both sides by 2:

| 15 - x | < 17/2

Now, we break this into two separate inequalities:

15 - x < 17/2 and 15 - x > -17/2

First, solve for x in the first inequality:

15 - x < 17/2

Subtract 15 from both sides:

-x < 17/2 - 15

-x < 17/2 - 30/2

-x < -13/2

Now, multiply both sides by -1 (remember to reverse the inequality sign when multiplying by a negative number):

x > 13/2

Next, solve for x in the second inequality:

15 - x > -17/2

Subtract 15 from both sides:

-x > -17/2 - 15

-x > -17/2 - 30/2

-x > -47/2

Now, multiply both sides by -1 (again, reverse the inequality sign when multiplying by a negative number):

x < 47/2

So, the second inequality is:

13/2 < x < 47/2

Now, we need to find the intersection of these two solution sets because both inequalities must be satisfied:

-62/9 < x < 62/9 and 13/2 < x < 47/2

The final solution is the intersection of these intervals:

13/2 < x < 47/2 and -62/9 < x < 62/9

So, the solution for the original compound inequality is:

-62/9 < x < 13/2 and 47/2 > x > 62/9

You can represent this solution on a number line or in interval notation as needed.