Question

X 5 ≥ 12 or x9 < 0 responses a) x ≥ 7 or x < 0x ≥ 7 or x < 0 b) x ≤ 7 or x > 0x ≤ 7 or x > 0 c) x ≤ − 7 or x > 0x ≤ − 7 or x > 0 d) x ≤ − 7 or x < 0

Answer 1

The given inequalities, assuming multiplication, suggest x should be at least 2.4 or negative. However, the student's question's options do not reflect this solution, indicating a possible error in the provided inequalities or the options themselves.

Step-by-step explanation:

The question revolves around solving inequalities and determining the set of solutions that satisfy given conditions. We have been provided with two inequalities:
1) x \( \times \) 5 \( \geq \) 12
2) x \( \times \) 9 < 0

Let's solve each inequality separately:

1. For the first inequality x \( \times \) 5 \( \geq \) 12, we divide both sides by 5 to isolate x, yielding x \( \geq \) 2.4. However, the original inequality seems to suggest a typo since it says 'X 5' which usually means 'x \( \times \) 5'. Assuming it's a multiplication sign, the solution would be as stated.
2. For the second inequality x \( \times \) 9 < 0, since 9 is a positive number, the inequality indicates that x must be a negative number to make the product less than zero. Thus, x < 0.

Combining the two solutions, we can say that x is a solution if:

• x \( \geq \) 2.4, which contradicts the options provided in the original question, or
• x < 0, which is an option in both the original question and this solution.

Given the options in the original question, none of them accurately reflects the proper solution derived from the inequalities provided. It seems that there's a mistake either in the inequalities or in the given options.