Question

Consider these three inequalities.

l. x/4<0
ll. 9x<-9
lll. 14≤3x+14

For which of these inequalities is x=0 a solution?

I only

III only

I and II

I and III

Answer 1

Let's evaluate each inequality to see if \( x = 0 \) is a solution.

1. For the first inequality \( \frac{x}{4} < 0 \):
- When \( x = 0 \), we have \( \frac{0}{4} < 0 \), which simplifies to \( 0 < 0 \). This is **false**. So, \( x = 0 \) is **not** a solution.

2. For the second inequality \( 9x < -9 \):
- When \( x = 0 \), we have \( 9(0) < -9 \), which simplifies to \( 0 < -9 \). This is **false**. So, \( x = 0 \) is **not** a solution.

3. For the third inequality \( 14 \leq 3x + 14 \):
- When \( x = 0 \), we have \( 14 \leq 3(0) + 14 \), which simplifies to \( 14 \leq 14 \). This is **true**. So, \( x = 0 \) is a solution.

Now let's summarize:
- \( x = 0 \) is a solution for **III only**.

Thus, the answer is **III only**.