Final answer:
To satisfy the inequality ax + 4 ≤ 3x + b, you need to choose values for a and b that make each statement true. When a = 5 and b = 7, the solution is x < -3. When a = 0 and b = 0, the inequality has no solution. When a = -2 and b = -6, the solution is x ≤ 2.
Step-by-step explanation:
To satisfy the inequality ax + 4 ≤ 3x + b, we need to choose values for a and b that make each statement true:
a. When a = 5 and b = 7, the solution is x < -3.
b. When a = 0 and b = 0, the inequality has no solution.
c. When a = -2 and b = -6, the solution is x ≤ 2.
For statement a, substituting the values a = 5, b = 7, and x = -3 into the inequality: 5(-3) + 4 ≤ 3(-3) + 7. Simplifying, we have -15 + 4 ≤ -9 + 7, which becomes -11 ≤ -2. Since this statement is true, the values a = 5 and b = 7 satisfy the inequality.
For statement b, substituting the values a = 0 and b = 0 into the inequality: 0x + 4 ≤ 3x + 0. Simplifying, we have 4 ≤ 3x. Since there is no value of x that makes this statement true, the inequality has no solution when a = 0 and b = 0.
For statement c, substituting the values a = -2 and b = -6 into the inequality: -2x + 4 ≤ 3x - 6. Simplifying, we have 4 + 6 ≤ 3x + 2x, which becomes 10 ≤ 5x. Dividing both sides by 5, we get 2 ≤ x. Since this statement is true, the values a = -2 and b = -6 satisfy the inequality.