# How do you evaluate 1/2[(3x+1) - (2-x)]?

Mar 30, 2018

$2 x - \frac{1}{2}$

#### Explanation:

Use brackets hierarchy: the innermost brackets are $3 x + 1$ and $2 - x$, but they don't involve similar terms, so we have nothing to do.

Then, the square brackets: we need to subtract the two quantities above, obtaining

$\left(3 x + 1\right) - \left(2 - x\right) = 3 x + 1 - 2 + x = 4 x - 1$

Finally, we divide everythin by two, as the outer $\frac{1}{2}$ suggests:

$\frac{4 x}{2} - \frac{1}{2} = 2 x - \frac{1}{2}$