To solve the inequality \( 1.4x - 3.4 > 5 \frac{1}{4} \), we first convert \( 5 \frac{1}{4} \) to an improper fraction:
\[ 5 \frac{1}{4} = 5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4} \]
Now we rewrite the inequality:
\[ 1.4x - 3.4 > \frac{21}{4} \]
Next, we convert \( 1.4 \) and \( 3.4 \) to fractions for easier calculations:
\[ 1.4 = \frac{14}{10} = \frac{7}{5}, \quad 3.4 = \frac{34}{10} = \frac{17}{5} \]
Now substitute these fractions into the inequality:
\[ \frac{7}{5}x - \frac{17}{5} > \frac{21}{4} \]
To eliminate the fractions, we can multiply the entire inequality by \( 20 \) (the least common multiple of 5 and 4):
\[ 20\left(\frac{7}{5}x - \frac{17}{5}\right) > 20\left(\frac{21}{4}\right) \]
This simplifies to:
\[ 4 \cdot 7x - 4 \cdot 17 > 5 \cdot 21 \]
\[ 28x - 68 > 105 \]
Now we add \( 68 \) to both sides:
\[ 28x > 173 \]
Finally, divide both sides by \( 28 \):
\[ x > \frac{173}{28} \]
Calculating the value of \( \frac{173}{28} \):
\[ \frac{173}{28} \approx 6.17857 \]
The simplified decimal is approximately \( 6.18 \).
Since none of the given options are correct, here’s the answer summarized:
\[ x > \frac{173}{28} \quad \text{(or approximately \( 6.18 \))} \]
If you need further assistance with this or any other math problem, feel free to ask!
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