Question

Solve the inequation:

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

and x$\in$R.

• A. $\{x:x\in Randx>6\}$
• B. $\{x:x\in Randx\le 6\}$
• C. $\{x:x\in Randx\ge 6\}$
• D. $\{x:x\in Randx>6\}$

Answer 1

The correct option is C

$\{x:x\in Randx\ge 6\}$

Given that:

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

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

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

$\Rightarrow 7\le \frac{18x-11x}{6}$

$\Rightarrow 7\le \frac{7x}{6}$

$\Rightarrow x\ge 6$

Since x$\in$R:

$\{x:x\in Randx\ge 6\}$