Question

Solve the inequality for x, assuming that a, b, and c are positive constants.
(a) a(bx − c) ≥ bc

(Choose the correct answer)
1.[0, c/a]
2. (c/b, bc/a)
3. [c/a + c/b, infinity)
4. (bc, a(b-c)/bc]
5. (-infinity, c/b]

Answer 1

\[a(bx-c)\ge bc\\abx-ac\ge bc\\abx\ge ac+bc\\x\ge \frac{ac}{ab}+\frac{bc}{ab}\\x\ge\frac{c}{b}+\frac{c}{a}\]

Answer 2

Thank you so much! It makes a lot more sense now