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.

Question

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Answer 1

To solve the inequality \( 47x - 27 > 57 \), we first add 27 to both sides:

\[ 47x - 27 + 27 > 57 + 27 \] \[ 47x > 84 \]

Next, we divide both sides by 47:

\[ x > \frac{84}{47} \]

Now we simplify \( \frac{84}{47} \) to a mixed number. First, we divide 84 by 47:

\[ 84 \div 47 = 1 \quad \text{with a remainder of } 37 \]

So, we can express \( \frac{84}{47} \) as a mixed number:

\[ \frac{84}{47} = 1 \frac{37}{47} \]

Finally, we write the final answer with \( x \) first:

\[ x > 1 \frac{37}{47} \]