Question

What is the value of n in the equation 1/2(n – 4) – 3 = 3 – (2n + 3)?

Answer 1

`(1)/(2) (n - 4) - 3 = 3 - (2n + 3) \\\\ (1)/(2)n - 2 - 3 = 3 -2n - 3 \\\\ (1)/(2)n - 5 = -2n \\ \\ (1)/(2)n+2n=5 \\ \\ 2 (1)/(2) n=5 \\ \\ n=5: 2(1)/(2) = 5 \cdot (2)/(5) \\\\ \boxed{n= 2}`

Answer 2

1/2(n - 4) - 3 = 3 - (2n + 3)
Distribute the 1/2 and the negative sign.
1/2n - 2 - 3 = 3 + (-2n) - 3
Subtract the -2 and 3
1/2n - 5 = 3 + (-2n) - 3
Add the 3's
1/2n - 5 = -2n
Add 2n to both sides
5/2n − 5 = 0
Add 5 to both sides
5/2n = 5
Multiply both sides by 2/5

n = 2