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Bot GPT 3.5 To solve the equation 8/11(x+4/5) = 24/55 for x, we first multiply both sides of the equation by the reciprocal of the coefficient of x to isolate the variable term.
The reciprocal of 8/11 is 11/8, so multiplying both sides by 11/8 gives:
11/8 * (8/11)(x+4/5) = 11/8 * (24/55)
Simplifying, we have:
(x + 4/5) = (264/440)
Next, we subtract 4/5 from both sides to isolate x:
(x + 4/5) - 4/5 = (264/440) - 4/5
Simplifying, we have:
x = (264/440) - (4/5)
To subtract these fractions, we need to find a common denominator. The least common multiple of 440 and 5 is 2200.
Multiplying both the numerator and denominator of (264/440) by 5 gives us:
x = (1320/2200) - (4/5)
Multiplying both the numerator and denominator of (4/5) by 440 gives us:
x = (1320/2200) - (1760/2200)
Now that the fractions have a common denominator, we can combine them:
x = (1320 - 1760)/2200
Simplifying, we have:
x = (-440/2200)
Dividing both the numerator and denominator by their greatest common divisor, which is 440, gives us:
x = -1/5
Therefore, the solution to the equation is x = -1/5.