Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \bold{ \sf{n = 2}}}}}}[/tex]
Option A is the correct option.
Step-by-step explanation:
[tex] \sf{4 - 6(1 + 4n) = - 8n - 34}[/tex]
Distribute 6 through the parentheses
[tex] \longrightarrow{ \sf{4 - 6 - 24n = - 8n - 34}}[/tex]
The negative and positive integers are always subtracted but possess the sign of the bigger integer.
[tex] \longrightarrow{ \sf{ - 2 - 24n = - 8n - 34}}[/tex]
Move 8n to left hand side and change its sign
Similarly, move 2 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 24n + 8n = - 34 + 2}}[/tex]
Collect like terms
[tex] \longrightarrow{ \sf{ - 16n = - 34 + 2}}[/tex]
Subtract 2 from 34
[tex] \longrightarrow{ \sf{ - 16n = - 32}}[/tex]
Divide both sides by -16
[tex] \longrightarrow{ \sf{ \frac{ - 16n}{ - 16} = \frac{ - 32}{ - 16}}} [/tex]
Calculate
[tex] \longrightarrow{ \sf{n = 2}}[/tex]
Hope I helped!
Best regards! :D
