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Solve 47x−27>57. Write the rational number in your answer as a mixed number. Make sure to write your inequality so that x comes first.%0D%0A%0D%0ANote: You will find the option to add a >%0D%0A>%0D%0A, <%0D%0A<%0D%0A, ≥%0D%0A≥%0D%0A, or ≤%0D%0A≤%0D%0A symbol in the Comparison (<)%0D%0A(%0D%0A<%0D%0A)%0D%0A keyboard.%0D%0A%0D%0A(1 point)

1 answer

To solve the inequality 47x - 27 > 57, we can follow these steps:

1. Add 27 to both sides of the inequality to isolate the variable x:
47x - 27 + 27 > 57 + 27
47x > 84

2. Divide both sides of the inequality by 47:
(47x)/47 > 84/47
x > 84/47

Now, let's express the rational number 84/47 as a mixed number:
Divide 84 by 47:
84 ÷ 47 = 1 remainder 37

So, the mixed number representation of 84/47 is 1 and 37/47.

Therefore, the solution to the inequality is:
x > 1 37/47