Question

What is the solution for the inequality (a + c) x > b^2 in terms of x, a, b, and c?

a) x > (b^2) / (a + c)
b) x < (b^2) / (a + c)
c) x = (b^2) / (a + c)
d) x ≥ (b^2) / (a + c)

Answer 1

The solution to the inequality (a + c) x > b^2 is x > (b^2) / (a + c), which is option a) assuming that a + c is positive. If a + c is negative, the inequality sign reverses.

Step-by-step explanation:

The solution to the inequality (a + c) x > b^2 in terms of x, assuming that a + c is positive, involves isolating x on one side of the inequality. First, you would divide both sides of the inequality by (a + c) to get x > (b^2) / (a + c), making sure that (a + c) is not zero to avoid division by zero. The solution to the inequality (a + c) x > b^2 is option a) x > (b^2) / (a + c).

If a + c is negative, we must reverse the inequality when we divide both sides by (a + c), so the solution would then be x < (b^2) / (a + c).