Question

4 - 6(1 + 4n) = -8n - 34 A) {2} B) {-16} C) { 5 } D) {7} show your work

Answer 1

the answer is n=2 (A)

hope this helps

Answer 2

`\boxed{ \bold{ \huge{ \boxed{ \bold{ \sf{n = 2}}}}}}`

Option A is the correct option.

Explanation:

`\sf{4 - 6(1 + 4n) = - 8n - 34}`

Distribute 6 through the parentheses

`\longrightarrow{ \sf{4 - 6 - 24n = - 8n - 34}}`

The negative and positive integers are always subtracted but possess the sign of the bigger integer.

`\longrightarrow{ \sf{ - 2 - 24n = - 8n - 34}}`

Move 8n to left hand side and change its sign

Similarly, move 2 to right hand side and change it's sign

`\longrightarrow{ \sf{ - 24n + 8n = - 34 + 2}}`

Collect like terms

`\longrightarrow{ \sf{ - 16n = - 34 + 2}}`

Subtract 2 from 34

`\longrightarrow{ \sf{ - 16n = - 32}}`

Divide both sides by -16

`\longrightarrow{ \sf{ ( - 16n)/( - 16) = ( - 32)/( - 16)}}`

Calculate

`\longrightarrow{ \sf{n = 2}}`

Hope I helped!

Best regards! :D