Question

Please help asap!!! :) 84 points if done correctly.

Answer 1

`\boxed{\checkmark}\;\;52 = 8n + 4`

`\boxed{\checkmark}\;\;4(2n + 1) = 52`

`\boxed{\checkmark}\;\;4 = 52 - 8n`

`\boxed{\phantom{\checkmark}}\;\;4n = 48`

`\boxed{\checkmark}\;\;n = 6`

Explanation:

To determine if the equations are equivalent, solve the equations for n.

Option 1

`\begin{aligned}\implies 52&=8n+4\\52-4&=8n+4-4\\48&=8n\\48/ 8&=8n / 8\\6&=n\\n&=6\end{aligned}`

Option 2

`\begin{aligned}\implies 4(2n+1)&=52\\8n+4&=52\\8n+4-4&=52-4\\8n&=48\\8n / 8&=48 / 8\\n&=6\end{aligned}`

Option 3

`\begin{aligned}\implies 4&=52-8n\\4+8n&=52-8n+8n\\4+8n&=52\\4+8n-4&=52-4\\8n&=48\\8n / 8&=48 / 8\\n&=6\end{aligned}`

Option 4

`\begin{aligned}\implies 4n&=48\\4n / 4&=48 / 4\\n&=12\end{aligned}`

Option 5

`n=6`

Therefore, the equations that are equivalent are:

• 52 = 8n + 4
• 4(2n + 1) = 52
• 4 = 52 - 8n
• n = 6