How do you solve -32- 4n = 5( n - 1)?

May 14, 2018

$n = - 3$

Explanation:

$- 32 - 4 n = 5 \left(n - 1\right)$

First, distribute 5 to (n -1), per PEMDAS. You should now have:

$- 32 - 4 n = 5 n - 5$

We want to negate the lowest variable in order to solve for n. Add 4n to each side to negate -4n. You should now have:

$- 32 = 9 n - 5$

Add 5 to each side to negate -5.

$- 27 = 9 n$

Divide by 9 to isolate for n.

$- \frac{27}{9}$ = $- 3$ = $n$

$n$ = $- 3$

May 14, 2018

$n = - 3$

Explanation:

To solve for the variable $n$ in the equation -32-4n=5(n-1)

Begin by using the distributive property to eliminate the parenthesis.

-32 -4n =5(n-1)

$- 32 - 4 n = 5 n - 5$

Now use the additive inverse to place the variable terms on the same side of the equation.

$- 32 - 4 n - 5 n = \cancel{5 n} - 5 \cancel{- 5 n}$

$- 32 - 9 n = - 5$

Now use the additive inverse to place the numeric terms on the same side of the equation.

$\cancel{- 32} - 9 n \cancel{+ 32} = - 5 + 32$

$- 9 n = 27$

Use the multiplicative inverse to isolate the variable.

$\frac{\left(\cancel{-} 9\right) n}{\cancel{- 9}} = \frac{27}{-} 9$

$n = - 3$