Problem 4 · The operation a#b
Evaluate and solve a linear equation.
Integer answer, at most 4 digitsIf we define the operation $a \# b = a \cdot b - a + b$, and we know that $3 \# 9 = 7 \# x$, what number is $x$?
Copa Cangur · SCM
Easy
Closed answer
Reasoned solution
Key idea: evaluate the left-hand side and leave the right-hand side in terms of $x$.
$$3 \# 9 = 27 - 3 + 9 = 33, \qquad 7 \# x = 7x - 7 + x = 8x - 7.$$
$$8x - 7 = 33 \;\Longrightarrow\; x = 5.$$
Answer: 5