Question

Solve the inequation $12+1\frac{5}{6}x\le 5+3x,xϵR$.

Answer 1

$12+1\frac{5}{6}x\le 5+3x$

$\Rightarrow 12+\frac{11x}{6}\le 5+3x$

Multiply both sides by $6,$ we get

$12\times 6+\frac{11x}{6}\times 6\le 5\times 6+3x\times 6$

$\Rightarrow 72+11x\le 30+18x$

Add $-18x$ and $-72$ on both sides, we get

$72+11x-72-18x\le 30+18x-72-18x$

$\Rightarrow 11x-18x\le 30-72$

$\Rightarrow -7x\le -42$

Dividing both sides by $-7$, we get

$x\ge 6$