Find the range of values of x for which \(\frac{(x+2)}{4}-\frac{2x-3}{3}<4\)
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Correct Answer: Option A
Explanation:
\(\frac{x + 2}{4} - \frac{2x - 3}{3} < 4\)
\(\frac{3(x + 2) - 4(2x - 3)}{12} < 4\)
\(3x + 6 - 8x + 12 < 48\)
\(18 - 5x < 48 \implies -5x < 48 - 18\)
\(-5x < 30 \implies x > -6\)
\(\frac{x + 2}{4} - \frac{2x - 3}{3} < 4\)
\(\frac{3(x + 2) - 4(2x - 3)}{12} < 4\)
\(3x + 6 - 8x + 12 < 48\)
\(18 - 5x < 48 \implies -5x < 48 - 18\)
\(-5x < 30 \implies x > -6\)