(7 3/22-x)+4 9/44= 9 8/33 -4 2/77

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To solve this equation, we first need to simplify both sides of the equation.

On the left side:

7 3/22 - x = 7 66/22 - x = 7 3 - x

So, we have:

(7 3-x) + 4 9/44 = 4 * (7 3-x) + 9/11 = 28 - 4x + 9/11

On the right side:

9 8/33 - 4 2/77 = 9 254/77 - 4/77 = 9 250/77

So, the equation becomes:

28 - 4x + 9/11 = 9 250/77

Now, we need to find a common denominator for the fractions on both sides. The least common multiple of 11 and 77 is 77, so we can rewrite the equation as:

(28 7 - 4x 7 + 9) / 77 = 250

Now simplify the left side:

(196 - 28x + 9) / 77 = 250

Combine like terms:

(205 - 28x) / 77 = 250

Now, we can cross multiply:

205 - 28x = 250 * 77

205 - 28x = 19250

To solve for x, subtract 205 from both sides:

-28x = 19045

x = -19045 / -28

x ≈ 680.89

Therefore, the value of x is approximately 680.89.