Question

3x-4 <5 or 3x + 4≥ 25Which choice best describes the solution set?
-3 ≤ x <7
1 ≤ x < -7
x>3 or x ≤7
x < or x≥ 7

Answer 1

To solve the inequalities \(3x - 4 < 5\) and \(3x + 4 \geq 25\), we will solve each one separately:

1. **For the inequality \(3x - 4 < 5\)**:
\[
3x - 4 < 5
\]
Add 4 to both sides:
\[
3x < 9
\]
Divide by 3:
\[
x < 3
\]

2. **For the inequality \(3x + 4 \geq 25\)**:
\[
3x + 4 \geq 25
\]
Subtract 4 from both sides:
\[
3x \geq 21
\]
Divide by 3:
\[
x \geq 7
\]

So, combining both results, the solution set is:
\[
x < 3 \quad \text{or} \quad x \geq 7
\]

Now let’s analyze the provided options to see which one matches our solution set:

- \(-3 ≤ x < 7\) - **Not correct** since it doesn't include \(x \geq 7\).
- \(1 ≤ x < -7\) - **Not correct** since the range is invalid.
- \(x > 3 \text{ or } x ≤ 7\) - **Not correct** since it doesn't match our conditions.
- \(x < 3 \text{ or } x \geq 7\) - **This is correct.**

Therefore, the choice that best describes the solution set is:
**\(x < 3 \text{ or } x \geq 7\)**.

If this exact option is not available, please double-check the list of choices.