Solve for n -5(n-1)=7(n+3)

$- 5 (n - 1) = 7 (n + 3)$

Step 1

Simplify $- 5 (n - 1)$ .

Start simplifying.

$0 + 0 - 5 (n - 1) = 7 (n + 3)$

Simplify by adding zeros.

$- 5 (n - 1) = 7 (n + 3)$

Apply the distributive property.

$- 5 n - 5 \cdot - 1 = 7 (n + 3)$

Multiply $- 5$ by $- 1$ .

$- 5 n + 5 = 7 (n + 3)$

Step 2

Simplify $7 (n + 3)$ .

Apply the distributive property.

$- 5 n + 5 = 7 n + 7 \cdot 3$

Multiply $7$ by $3$ .

$- 5 n + 5 = 7 n + 21$

Step 3

Move all terms containing $n$ to the left side of the equation.

Subtract $7 n$ from both sides of the equation.

$- 5 n + 5 - 7 n = 21$

Subtract $7 n$ from $- 5 n$ .

$- 12 n + 5 = 21$

Step 4

Move all terms not containing $n$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$- 12 n = 21 - 5$

Subtract $5$ from $21$ .

$- 12 n = 16$

Step 5

Divide each term in $- 12 n = 16$ by $- 12$ and simplify.

Divide each term in $- 12 n = 16$ by $- 12$ .

$\frac{- 12 n}{- 12} = \frac{16}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 n}{- 12} = \frac{16}{- 12}$

Divide $n$ by $1$ .

$n = \frac{16}{- 12}$

Simplify the right side.

Cancel the common factor of $16$ and $- 12$ .

Factor $4$ out of $16$ .

$n = \frac{4 (4)}{- 12}$

Cancel the common factors.

Factor $4$ out of $- 12$ .

$n = \frac{4 \cdot 4}{4 \cdot - 3}$

Cancel the common factor.

$n = \frac{4 \cdot 4}{4 \cdot - 3}$

Rewrite the expression.

$n = \frac{4}{- 3}$

Move the negative in front of the fraction.

$n = - \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{4}{3}$

Decimal Form:

$n = - 1.\overline{3}$

Mixed Number Form:

$n = - 1 \frac{1}{3}$

Solve for n -5(n-1)=7(n+3)

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