Simplify 3-1/2(2x-4y)-(x+y)

$3 - \frac{1}{2} (2 x - 4 y) - (x + y)$

Step 1

Simplify each term.

Apply the distributive property.

$3 - \frac{1}{2} (2 x) - \frac{1}{2} (- 4 y) - (x + y)$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$3 + \frac{- 1}{2} (2 x) - \frac{1}{2} (- 4 y) - (x + y)$

Factor $2$ out of $2 x$ .

$3 + \frac{- 1}{2} (2 (x)) - \frac{1}{2} (- 4 y) - (x + y)$

Cancel the common factor.

$3 + \frac{- 1}{2} (2 x) - \frac{1}{2} (- 4 y) - (x + y)$

Rewrite the expression.

$3 - 1 x - \frac{1}{2} (- 4 y) - (x + y)$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$3 - 1 x + \frac{- 1}{2} (- 4 y) - (x + y)$

Factor $2$ out of $- 4 y$ .

$3 - 1 x + \frac{- 1}{2} (2 (- 2 y)) - (x + y)$

Cancel the common factor.

$3 - 1 x + \frac{- 1}{2} (2 (- 2 y)) - (x + y)$

Rewrite the expression.

$3 - 1 x - 1 (- 2 y) - (x + y)$

Multiply $- 2$ by $- 1$ .

$3 - 1 x + 2 y - (x + y)$

Rewrite $- 1 x$ as $- x$ .

$3 - x + 2 y - (x + y)$

Apply the distributive property.

$3 - x + 2 y - x - y$

Step 2

Simplify by adding terms.

Subtract $x$ from $- x$ .

$3 - 2 x + 2 y - y$

Subtract $y$ from $2 y$ .

$3 - 2 x + y$

Move $3$ .

$- 2 x + y + 3$