The binary operation \(\ast\) is defined by x \(\ast\) y = xy - y - x for all real values x and y. If x \(\ast\) 3 = 2\(\ast\) x, find x
A
-1
B
4
C
1
D
5
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
x \(\ast\) y = xy - y - x, x \(\ast\) 3 = 3x - 3 - x = 2x - 3
2 \(\ast\) x = 2x - x - 2 = x - 2
∴ 2x - 3 = x - 2
x = -2 + 3
= 1
Source: Myschool Past Questions Archive (Record #30715)