Question

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

Answer 1

Distribute 1/2 to (n – 4):


`(1)/(2) * n = (1)/(2)n`

`(1)/(2) * -4 = -2`

Subtract (2n + 3):


`- (2n + 3) = -2n -3`

Your equation should now look like this:


`(1)/(2)n - 2 - 3 = 3 - 2n - 3`

Combine like terms on both sides:


`-2 - 3 = -5`

`3 - 3 = 0`

`(1)/(2)n - 5 = -2n`

Subtract 1/2n from both sides:


`-5 = -(5)/(2)n`

Divide both sides by -5/2 to get n by itself:


`n = 2`

The value of n is 2.

Answer 2

`(1)/(2)(n-4)-3=3-(2n+3)\\\\\\(1)/(2)(n-4)-3=3-2n-3\\\\\\(1)/(2)(n-4)-3=-2n\qquad|\cdot2\\\\\\n-4-6=-4n\\\\n-10=-4n\qquad|+10\\\\n-10+10=-4n+10\\\\n=-4n+10\qquad|+4n\\\\n+4n=-4n+4n+10\\\\5n=10\qquad|:5\\\\\boxed{n=2}`