JAMB 1997 · UME · Q22

Binary operations

If $x * y = x + y - xy$ , find $x$ when $(x * 2) + (x * 3) = 68$ .

Worked solution (try it first)

Use the rule with $y = 2$ : $x * 2 = x + 2 - 2x = 2 - x$ .
With $y = 3$ : $x * 3 = x + 3 - 3x = 3 - 2x$ .
Add them: $5 - 3x = 68$ .
Take 5 from both sides: $-3x = 63$ , so $x = -21$ , option D.

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