# If 2x+ 1/3x=6, then the value of 3x + 1/2x will be

(a) 4

(b) 8

(c) 9

(d) 12

**Answer: (c) 9**

**Solution:-**

Let the value of (3 X + 1/2 X) be Y.

3 X + 1/2 X = Y

6 X^2 + 1 = 2 X Y

6 X^2 – 2 X Y + 1 = 0 …………………. (1)

2 X + 1/3 X = 6

6 X^2 + 1 = 18 X

6 X^2 – 18 X + 1 = 0 ………………… (2)

Equation (2) subtract from equation (1),

Then, 6 X^2 – 2 X Y + 1 – 6 X^2 + 18 X – 1 = 0

-2 X Y + 18 X = 0

– 2 X Y = – 18 X

2 Y = 18

Y = 18/2

Y = 9

Then, the value of Y = 3 X + 1/2 X = 9.

Hence, the correct answer is option (c) 9.