Question

Solve the in-equation: 12 + 1 5/6 x ≤ 5 + 3x and x ∈ R.​

Answer 1

$\tt12 + 1 \frac{5}{6} x \leqslant 5 + 3x \\ \\ \tt12 - 5 - 3x + 1\frac{5}{6} x\leqslant 5 + 3x - 5 - 3x \\ \\ \tt7 - 3x + \frac{11}{6} x \leqslant 0 \\ \\ \tt7 - \frac{18x - 11x}{6} \leqslant 0 \\ \\ \tt 7 - \frac{7x}{6} \leqslant 0 \\ \\ \tt \frac{42 - 7x}{6} \leqslant 0 \\ \\ \tt\bigg( \frac{42 - 7x}{ \cancel6} \bigg) \times \cancel6 \leqslant 0 \times 6 \\ \\ \tt42 - 7x \leqslant 0 \\ 42 \: \cancel{ - 7x} \cancel{ + 7x} \leqslant 0 + 7x \\ 42 \leqslant 7x \\ \\ \tt \frac{42}{7} \leqslant \frac{ \cancel7x}{ \cancel7} \\ \\ \tt \red{6 \leqslant x}$