Let's call Q the initial charge of the object, which is:
[tex]Q=-4[/tex]
When it breaks, the two pieces will have charge [tex]Q_1[/tex] and [tex]Q_2[/tex], and since the total charge must be conserved, the sum of these two charges must be equal to the initial charge of the object:
[tex]Q=Q_1+Q_2[/tex]
We also know the charge of one of the two pieces:
[tex]Q_1=-5[/tex]
So, by substituting Q and Q1 into the equation, we can find the charge of the second piece, Q2:
[tex]Q_2=Q-Q_1=-4 -(-5)=-4+5=+1[/tex]
