Question

Please help, solve for x and n

Answer 1

Answer:

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

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

Step-by-step explanation:

1. $\sf{ \frac{6}{x + 1} = \frac{3}{x} }$

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

$\dashrightarrow{ \sf{ \frac{3x}{3} = \frac{3}{3} }}$

Calculate

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

The value of x is 1

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2. $\sf{ \frac{2}{6} = \frac{2n + 8}{n - 1}}$

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

$\dashrightarrow{ \sf{ \frac{ - 10n}{ - 10} = \frac{50}{ - 10} }}$

Calculate

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

The value of n is -5 .

Hope I helped!

Best regards! :D