SOLUTION
(2). We are given the equation
[tex]\frac{3j+k}{2}=15-4k[/tex]
And we want to prove that
[tex]\begin{gathered} j=10-3k \\ \end{gathered}[/tex]
This becomes
[tex]\text{Statement }\frac{3j+k}{2}=15-4k[/tex]
Reason: Given
[tex]\begin{gathered} \text{Multiplying 2 by both sides } \\ \text{Statement }\frac{3j+k}{2}\times2=(15-4k)2 \\ 3j+k=30-8k \end{gathered}[/tex]
Reason: Multiplication property of equality.
[tex]\begin{gathered} \text{Subtracting k from both sides } \\ \text{Statement } \\ 3j+k-k=30-8k-k \\ 3j=30-9k \end{gathered}[/tex]
Reason: Subtraction property.
[tex]\begin{gathered} \text{Dividing }both\text{ sides by 3} \\ \text{Statement } \\ \frac{3j}{3}=\frac{30-9k}{3} \\ j=\frac{3(10-3k)}{3}\text{ note that 3 cancels out} \\ j=10-3k \end{gathered}[/tex]
Reason: Division property of equality
