Solve each of the following system of equations in R. 10. 11 − 5x > −4,

Solution:

We have,

$11-5 x>-4$

$\Rightarrow-5 x>-4-11$

$\Rightarrow-5 x>-15$

$\Rightarrow 5 x<15 \quad$ [Multiplying both sides by $-1$ ]

$\Rightarrow x<\frac{15}{5}$

$\Rightarrow x<3$

$\Rightarrow x \in(-\infty, 3) \quad \ldots$ (i)

Als $o, 4 x+13 \leq-11$

$\Rightarrow 4 x \leq-11-13$

$\Rightarrow 4 x \leq-24$

$\Rightarrow x \leq-6$

$\Rightarrow x \in(-\infty,-6] \quad \ldots$ (ii)

Hence, the solution of the given set of inequalities is the intersection of (i) and (ii).

$(-\infty 3) \cap(-\infty,-6]=(-\infty,-6]$

Hence, the solution of the given set of inequalities is $(-\infty,-6]$.