Question

( 8 2/5 : x + 3 5/9) : 4 1/6 = 1 1/3

Answer 1

Відповідь:

Покрокове пояснення:

переведемо все в неправильні дроби

(42/5 :х +32/9): 25/6 =4/3

42/5 : х + 32/9 = 4/3×25/6

42/5:х = 50/9 - 32/9

42/5 : х =18/9

42/5 : х =2

х= 42/5 : 2

х= 42/10

х=4,2 = 4 1/5

Answer 2

To solve the equation:

(8 2/5 : (x + 3 5/9)) : 4 1/6 = 1 1/3

Let's break it down step by step:

1. Convert all mixed numbers into improper fractions: 8 2/5 = (8 * 5 + 2) / 5 = 42/5 3 5/9 = (3 * 9 + 5) / 9 = 32/9 4 1/6 = (4 * 6 + 1) / 6 = 25/6 1 1/3 = (1 * 3 + 1) / 3 = 4/3

2. Rewrite the equation: (42/5 : (x + 32/9)) : 25/6 = 4/3

3. Simplify the expression within the parentheses: (42/5 : (x + 32/9)) = (42/5) / (x + 32/9) = (42/5) * (9/32) / (x + 32/9) = (42 * 9) / (5 * 32) / (x + 32/9) = 378/160 / (x + 32/9) = 189/80 / (x + 32/9)

4. Rewrite the equation: (189/80 / (x + 32/9)) : 25/6 = 4/3

5. Invert and multiply: (189/80 / (x + 32/9)) * (6/25) = 4/3

6. Simplify the expression: (189/80) * (6/25) / (x + 32/9) = 4/3

7. Multiply the numerators and denominators: (1134/200) / (x + 32/9) = 4/3

8. Invert and multiply: (1134/200) * (3/4) = (x + 32/9)

   Simplify the expression: (850.5/200) = (x + 32/9)

9. Simplify the left side: 850.5/200 = 4.2525

   Set the right side equal to the result: 4.2525 = (x + 32/9)

10. Subtract 32/9 from both sides: 4.2525 - 32/9 = x

11. Convert 4.2525 to a fraction: 4.2525 = 4 + 0.2525 = 4 + 2525/10000 = 4 + 505/2000 = 4 + 101/400

    Substitute the value back into the equation: 101/400 - 32/9 = x

12. Find a common denominator for 400 and 9, which is 3600: (101 * 9)/3600 - (32 * 400)/3600 = x (909/3600) - (12800/3600) = x

13. Combine the fractions: (909 - 12800)/3600 = x (-11891/3600) = x

Therefore, the solution to the equation is: x = -11891/3600, which can be simplified to approximately -3.3036.