Question

The solution set of the inequalities $3x-7>2(x-6)$ and $6-x>11-2x$, is

• A. $(-5,\infty )$
• B. $[5,\infty )$
• C. $(5,\infty )$
• D. $[-5,\infty )$

Answer 1

Answer: (C)

We have $3x-7>2(x-6)$
$\Rightarrow 3x-7>2x-12$
Transferring the term $2x$ to $L.H.S.$ and the term $\left(-7\right)$ to $R.H.S.,3x-2x>-12+7$
$\Rightarrow x>-5...\left(i\right)$
and $6-x>11-2x$
Transferring the term $\left(-2x\right)$ to $L.H.S$. and the term 6 to $R.H.S.,-x+2x>11-6$
$\Rightarrow x>5...\left(ii\right)$
Draw the graph of inequations (i) and (ii) on the number line,

Hence, solution set of the equations are real numbers, $x$ lying on greater than 5 excluding 5. i.e., $x>5\therefore$ Solution set is $(5,\infty )$