question_answer

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) \[[-5,\infty )\]

Correct Answer: C

Solution :

[c] We have \[3x-7>2(x-6)\]

\[\Rightarrow 3x-7>2x-12\]

Transferring the term 2x to L.H.S. and the term (-7) to R.H.S., \[3x-2x>-12+7\]

\[\Rightarrow x>-5\]                                            ?. (i)

And \[6-x>11-2x\]

Transferring the term \[(-2x)\] to L.H.S. and the term 6 to R.H.S.  \[-x+2x>11-6\]

\[\Rightarrow x>5\]                                             ? (ii)

Draw the graph of in equations (i) and (ii) o 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 \[(5,\,\,\,\infty )\]