Question

Which of the following inequalities would have solutions of
?
​
​Mark all that apply.
A
s ≥ − 3s\ \geq \ -\ 3s ≥ − 3
B
r ≤ 3r\ \leq \ 3r ≤ 3
C
v > −5v\ >\ -5v > −5
D
t < 2t\ <\ 2t < 2
E
w ≤ 2w\ \leq \ 2w ≤ 2

Answer 1

To determine which inequalities would have solutions of \(x\), you would need to analyze each inequality to see if \(x\) satisfies it for all possible values of \(x\).

Here’s the analysis for each choice:

A. \( s \geq -3 \)
This means \( s \) can be any number greater than or equal to \(-3\). This inequality will have solutions for many values of \(s\).
**Solution Set**: Valid for \(s \geq -3\).
- **Does it have solutions for \(x\)?** Yes.

B. \( r \leq 3 \)
This means \( r \) can be any number less than or equal to \(3\). This inequality will have solutions for many values of \(r\).
**Solution Set**: Valid for \(r \leq 3\).
- **Does it have solutions for \(x\)?** Yes.

C. \( v > -5 \)
This means \( v \) can be any number greater than \(-5\). This inequality allows many values of \(v\).
**Solution Set**: Valid for \(v > -5\).
- **Does it have solutions for \(x\)?** Yes.

D. \( t < 2 \)
This means \( t \) can be any number less than \(2\). This inequality has many solutions.
**Solution Set**: Valid for \(t < 2\).
- **Does it have solutions for \(x\)?** Yes.

E. \( w \leq 2 \)
This means \( w \) can be any number less than or equal to \(2\). This inequality has many solutions.
**Solution Set**: Valid for \(w \leq 2\).
- **Does it have solutions for \(x\)?** Yes.

Thus, all inequalities A, B, C, D, and E have solutions.

The answer is: **A, B, C, D, E**.