Solve each of the following system of equations in R. 8. 5x − 1 < 24, 5x + 1 > −24
Question:

Solve each of the following system of equations in R.

8. 5x − 1 < 24, 5x + 1 > −24

Solution:

$5 x-1<24$

$\Rightarrow 5 x<24+1$

$\Rightarrow x<5$

$\Rightarrow x \in(-\infty, 5)$

Also, $5 x+1>-24$

$\Rightarrow 5 x>-24-1$

$\Rightarrow x>-5$

$\Rightarrow x \in(-5, \infty) \quad \ldots$ (ii)

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

$(-\infty, 5) \cap(-5, \infty)=(-5,5)$

Thus, the solution of the given set of inequalities is $(-5,5)$.

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