Question

Solve for n in the literal equation a(n−4)+3=bn.

Answer 1

To solve for n start off by adding bn to both sides.
an - 4a + 3 + -bn = bn + -bn
an - bn - 4a + 3 = 0
Now, add -3 to both sides.
an - bn - 4a + 3 + -3 = 0 + -3
an - bn - 4a  = -3
Add 4a to both sides.
an - bn - 4a + 4a = -3 + 4a
an - bn = 4a - 3
Factor out variable n.
n(a-b) = 4a - 3
Divide both sides by a - b.
a(a-b) / a - b = 4a - 3 / a - b
Your final answer is:
n = 4a - 3 / a - b

Answer 2

Distribute a
an-4a+3=bn
minus bn from both sides
an-bn-4a+3=0
add 4a to both sides
an-bn+3=4a
minus 3 from both sides
an-bn=4a-3
undistribute n from left side
n(a-b)=4a-3
divide both sides by (a-b)
$n= \frac{4a-3}{a-b}$