JAMB 1998 · UME · Q22

Binary operations

The binary operation $*$ is defined by $x * y = xy - y - x$ for all real values of $x$ and $y$ . If $x * 3 = 2 * x$ , find $x$ .

Worked solution (try it first)

Use the rule with $y = 3$ : $x * 3 = 3x - 3 - x = 2x - 3$ .
Use it again with 2 first: $2 * x = 2x - x - 2 = x - 2$ .
Set them equal: $2x - 3 = x - 2$ .
Take $x$ from both sides and add 3: $x = 1$ , option C.

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