Question

Please help, solve for x and n

Answer 1

1.
`\boxed{ \bold{ \huge{ \boxed{ \sf{x = 1}}}}}`

2.
`\boxed{ \bold{ \huge{ \boxed{ \sf{n = - 5}}}}}`

Explanation:

1.
`\sf{ (6)/(x + 1) = (3)/(x) }`

Do cross multiplication

`\dashrightarrow{ \sf{6x = 3(x + 1)}}`

Distribute 3 through the parentheses

`\dashrightarrow{ \sf{6x = 3x + 3}}`

Move 3x to left hand side and change it's sign

`\dashrightarrow{ \sf{6x - 3x = 3}}`

Collect like terms

`\dashrightarrow{ \sf{3x = 3}}`

Divide both sides by 3

`\dashrightarrow{ \sf{ (3x)/(3) = (3)/(3) }}`

Calculate

`\dashrightarrow{ \sf{x = 1}}`

The value of x is 1

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2.
`\sf{ (2)/(6) = (2n + 8)/(n - 1)}`

Do cross multiplication

`\dashrightarrow{ \sf{2(n - 1) = 6(2n + 8)}}`

Distribute 2 through the parentheses

Similarly, distribute 6 through the parentheses

`\dashrightarrow{ \sf{2n - 2 = 12n + 48}}`

Move 12n to left hand side and change it's sign

Similarly, move 48 to right hand side and change it's sign

`\dashrightarrow{ \sf{2n - 12n = 48 + 2}}`

Collect like terms

`\dashrightarrow{ \sf{ - 10n = 48 + 2}}`

Add the numbers : 48 and 2

`\dashrightarrow{ \sf{ - 10n = 50}}`

Divide both sides by -10

`\dashrightarrow{ \sf{ ( - 10n)/( - 10) = (50)/( - 10) }}`

Calculate

`\dashrightarrow{ \sf{n = - 5}}`

The value of n is -5 .

Hope I helped!

Best regards! :D