Question

The equation |2ax-3|+|ax+1|+|5-ax|$=\frac{1}{2}$ possesses

• A. Infinite number of real solution for some $a\in R$
• B. Finite number of real solutions for some $a\in R$
• C. No real solution for some $a\in R$
• D. No real solution for all $a\in R$

Answer 1

The correct option is D No real solution for all $a\in R$

The equation |2ax-3|+|ax+1|+|5-ax|............
|2ax-3|+|ax+1|+|5-ax| $\ge |2ax-3+(-ax-1)+5-ax|\ge 1$
So no solution for $\frac{1}{2}$