Solve each of the following system of equations in R. 7. 2x + 5 ≤ 0, x − 3 ≤ 0
Question:

Solve each of the following system of equations in R.

7. 2x + 5 ≤ 0, x − 3 ≤ 0

Solution:

We have, $2 x+5 \leq 0$

$\Rightarrow 2 x \leq-5$

$\Rightarrow x \leq \frac{-5}{2}$

$\Rightarrow x \in\left(-\infty, \frac{-5}{2}\right] \quad \ldots(\mathrm{i})$

Also, $x-3 \leq 0$

$\Rightarrow x \leq 3$

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

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

$\left(-\infty, \frac{-5}{2}\right] \cap(-\infty, 3]=\left(-\infty, \frac{-5}{2}\right]$

Thus, the solution of the given set of inequalities is $\left(-\infty, \frac{-5}{2}\right]$.

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