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):

$\frac{1}{2} \times n = \frac{1}{2}n$
$\frac{1}{2} \times -4 = -2$

Subtract (2n + 3):

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

Your equation should now look like this:

$\frac{1}{2}n - 2 - 3 = 3 - 2n - 3$

Combine like terms on both sides:

$-2 - 3 = -5$
$3 - 3 = 0$
$\frac{1}{2}n - 5 = -2n$

Subtract 1/2n from both sides:

$-5 = -\frac{5}{2}n$

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

$n = 2$

The value of n is 2.

Answer 2

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