Answer
$x \ge \dfrac{c}{a}+\dfrac{c}{b}$
Work Step by Step
With a, b, and c positive constants, dividing and/or multiplying any if them to both sides of the inequality will not affect the inequality symbol
Divide $a$ to both sides to have:
$bx-c\ge\dfrac{bc}{a}$
Add $c$ to both sides to have:
$bx \ge \dfrac{bc}{a}+c$
Divide $b$ to both sides to have:
$x \ge \dfrac{\frac{bc}{a}+c}{b}
\\x \ge \dfrac{bc}{ab}+\dfrac{c}{b}
\\x \ge \dfrac{c}{a}+\dfrac{c}{b}$
