Final answer:
To solve the inequalities -15x+4≤ 109 and -6x+70 > -2, we find that the solution for the first is x ≥ -7 and for the second is x < 12. Since it is an OR statement, we combine the solutions to get -7 ≤ x < 12, which corresponds to answer choice (B).
Step-by-step explanation:
The student's question involves solving two inequalities and determining which solution set fits the given options (A) through (D). First, let's solve each inequality separately:
- For the inequality -15x + 4 ≤ 109, we add 15x to both sides and subtract 4 from both sides to get x ≥ -7.
- The second inequality is -6x + 70 > -2. By adding 6x to both sides and subtracting 70 from both sides, we get x < 12.
Since we have an OR statement, we combine the two solution sets. The complete solution is when x ≥ -7 OR x < 12, which implies that any value of x that satisfies either one or both of these conditions is a solution. Given the answer choices, the correct answer is (B) -7 ≤ x < 12.