Question

The solution set of inequalities :
x + 3 ≤ 0 and 2x + 5 ≤ 0; if x ∈ R is :

• A. (-x, -3)
• B. {..........., -5, -4, -3}
• C. (-x, -3]
• D. {-3, -2, -1, 0 ........}

Answer 1

The Correct Option is C

To find the solution set for the given inequalities, we solve each inequality separately and then find the intersection of the solutions.

1. Solve \(x + 3 \leq 0\):
\[x \leq -3\]

2. Solve \(2x + 5 \leq 0\):
\[2x \leq -5\]
\[x \leq -\frac{5}{2}\]

Now we have two inequalities: \(x \leq -3\) and \(x \leq -\frac{5}{2}\).
To find the intersection, take the more restrictive condition:
\[-3 \leq -\frac{5}{2}\] since \(-3\) is less than \(-\frac{5}{2}\), we take \(x \leq -3\).
The solution set is all \(x\) values satisfying this:

This can be represented in interval notation as:
\[(-\infty, -3]\]
This corresponds to the option:

(-x, -3]

.