Symbol
Using the new operator $\oplus$, can you solve this equation?
Age
11 to 14
Challenge level
Problem
We define $a\oplus b = ab + a + b $.
If $3 \oplus 5= 2 \oplus x$, what is the value of $x$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $7$
$3\oplus 5 = 3\times 5 + 3 +5 = 23$ and $2\oplus x = 2x + 2+ x= 3x + 2$.
These are equal, so $3x + 2 = 23$, i.e. $x=7$.