Q. The solutions of the system of inequalities $3 x-7<5+x$ and $11-5 x \leq 1$ on the number line is
Linear Inequalities
Solution:
Given inequalities are
$3 x-7 <5+x$...(i)
and $11-5 x \leq 1$...(ii)
From inequality (i), we have
$3 x-7 <5+x$
or $x <6$...(iii)
Also, from inequality (ii), we have
$11-5 x \leq 1 $
or $-5 x \leq-10 \text { i.e., } x \geq 2$.....(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.
