Question

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.

Answer 1

To solve the inequality 47x - 27 > 57, we can start by adding 27 to both sides of the inequality:

47x - 27 + 27 > 57 + 27

This simplifies to:

47x > 84

Next, we can divide both sides of the inequality by 47 to isolate x:

(47x)/47 > 84/47

Simplifying this further gives:

x > 1.7872340425531915

To write the rational number as a mixed number, we need to express it as a whole number plus a fraction. The whole number is 1, and the fraction can be calculated as follows:
0.7872340425531915 = 7872340425531915/10000000000000000

Simplifying the fraction by dividing both numerator and denominator by 5 gives:
7872340425531915/10000000000000000 = 1574468085106383/2000000000000000

Therefore, the rational number can be written as the mixed number:

1 + 1574468085106383/2000000000000000