Answer:
3.4981
Step-by-step explanation:
To find the value of x in the equation (x-2)/2024 + (x-3)/2023 + (x-4)/2022, we need to simplify and solve the equation.
To combine the fractions, we need to find a common denominator for the three terms, which is the least common multiple (LCM) of 2024, 2023, and 2022.
The LCM of these numbers is 9,293,656,184. We can rewrite the equation with the common denominator:
[(x-2)(2023)(2022) + (x-3)(2024)(2022) + (x-4)(2024)(2023)] / (2024)(2023)(2022)
Expanding and simplifying the equation:
[(x-2)(4117026) + (x-3)(4119048) + (x-4)(8306692)] / 9317676133384
Now we can further simplify the equation:
[4117026x - 8234052 + 4119048x - 12357144 + 8306692x - 33226768] / 9317676133384
Combining like terms:
(16572766x - 57979064) / 9317676133384
Now, we set this expression equal to zero and solve for x:
(16572766x - 57979064) / 9317676133384 = 0
16572766x - 57979064 = 0
16572766x = 57979064
x = 57979064 / 16572766
x ≈ 3.4981
Therefore, the value of x is approximately 3.4981.
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Answers & Comments
Answer:
3.4981
Step-by-step explanation:
To find the value of x in the equation (x-2)/2024 + (x-3)/2023 + (x-4)/2022, we need to simplify and solve the equation.
To combine the fractions, we need to find a common denominator for the three terms, which is the least common multiple (LCM) of 2024, 2023, and 2022.
The LCM of these numbers is 9,293,656,184. We can rewrite the equation with the common denominator:
[(x-2)(2023)(2022) + (x-3)(2024)(2022) + (x-4)(2024)(2023)] / (2024)(2023)(2022)
Expanding and simplifying the equation:
[(x-2)(4117026) + (x-3)(4119048) + (x-4)(8306692)] / 9317676133384
Now we can further simplify the equation:
[4117026x - 8234052 + 4119048x - 12357144 + 8306692x - 33226768] / 9317676133384
Combining like terms:
(16572766x - 57979064) / 9317676133384
Now, we set this expression equal to zero and solve for x:
(16572766x - 57979064) / 9317676133384 = 0
16572766x - 57979064 = 0
16572766x = 57979064
x = 57979064 / 16572766
x ≈ 3.4981
Therefore, the value of x is approximately 3.4981.