Question

The solutions of the system of inequalities $3x-7<5+x$ and $11-5x\le 1$ on the number line is

• A.
• B.
• C.
• D. None of the above

Answer 1

Answer: (B)

Given inequalities are
$3x-7<5+x$...(i)
and $11-5x\le 1$...(ii)
From inequality (i), we have
$3x-7<5+x$
or $x<6$...(iii)
Also, from inequality (ii), we have
$11-5x\le 1$
or $-5x\le -10\text{ i.e., }x\ge 2$.....(iv)
If we draw the graph of inequalities (iii) and (vi) on the number line, we see that the values of $x$, which are common to both, are shown by bold line in figure.