Question

1)x-|-5 3/7|=|-3 1/7|​

Answer 1

1. Число под модулем всегда положительное

т.е. х-|-5 3/7|=|-3 1/7| это то же самое, что:

х-(5 3/7)=3 1/7

2. решаем:

х-(5 3/7)=3 1/7

х=(3 1/7)+(5 3/7)

х=8 4/7

Ответ: 8 4/7

Answer 2

To solve the equation |x - |-5 3/7|| = |-3 1/7|, we'll break it down into separate cases based on the absolute values.

Case 1: x - |-5 3/7| = |-3 1/7| In this case, we have x minus the absolute value of -5 3/7 equals the absolute value of -3 1/7.

|-5 3/7| = 5 3/7 |-3 1/7| = 3 1/7

So, we have x - 5 3/7 = 3 1/7.

To simplify the equation, let's convert the mixed numbers to improper fractions: x - 5 3/7 = 3 1/7 x - 38/7 = 22/7

Now, we can solve for x: x = 22/7 + 38/7 x = (22 + 38)/7 x = 60/7 x = 8 4/7

Case 2: x - |-5 3/7| = -|-3 1/7| In this case, we have x minus the absolute value of -5 3/7 equals the negative of the absolute value of -3 1/7.

|-5 3/7| = 5 3/7 -|-3 1/7| = -3 1/7

So, we have x - 5 3/7 = -3 1/7.

Converting mixed numbers to improper fractions: x - 5 3/7 = -3 1/7 x - 38/7 = -22/7

Now, we can solve for x: x = -22/7 + 38/7 x = (38 - 22)/7 x = 16/7 x = 2 2/7

Therefore, the solutions to the equation |x - |-5 3/7|| = |-3 1/7| are x = 8 4/7 and x = 2 2/7.