Question

#2 complete each proof using the properties of equality. Not all rows may be used.

Answer 1

(2). We are given the equation

`(3j+k)/(2)=15-4k`

And we want to prove that

`\begin{gathered} j=10-3k \\ \end{gathered}`

This becomes

`\text{Statement }(3j+k)/(2)=15-4k`

Reason: Given

`\begin{gathered} \text{Multiplying 2 by both sides } \\ \text{Statement }(3j+k)/(2)*2=(15-4k)2 \\ 3j+k=30-8k \end{gathered}`

Reason: Multiplication property of equality.

`\begin{gathered} \text{Subtracting k from both sides } \\ \text{Statement } \\ 3j+k-k=30-8k-k \\ 3j=30-9k \end{gathered}`

Reason: Subtraction property.

`\begin{gathered} \text{Dividing }both\text{ sides by 3} \\ \text{Statement } \\ (3j)/(3)=(30-9k)/(3) \\ j=(3(10-3k))/(3)\text{ note that 3 cancels out} \\ j=10-3k \end{gathered}`

Reason: Division property of equality