The solution set of the inequation, $\frac{4 x+5}{7}-6<\frac{5(x+3)}{4}, x \in R$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\left(-\frac{253}{19}, \infty\right)$
$\frac{4x+5}{7} - 6 < \frac{5(x+3)}{4}$
$\frac{4x+5 - 42}{7} < \frac{5x+15}{4}$
$\frac{4x - 37}{7} < \frac{5x+15}{4}$
$4(4x - 37) < 7(5x + 15)$
$16x - 148 < 35x + 105$
$-148 - 105 < 35x - 16x$
$-253 < 19x$
$x > -\frac{253}{19}$
$\text{Solution set} = \left(-\frac{253}{19}, \infty\right)$