Solve for x 2x+7+(3-y)i=-4+6i

$2 x + 7 + (3 - y) i = - 4 + 6 i$

Apply the distributive property.

$2 x + 7 + 3 i - y i = - 4 + 6 i$

Move all terms not containing $x$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$2 x + 3 i - y i = - 4 + 6 i - 7$

Subtract $3 i$ from both sides of the equation.

$2 x - y i = - 4 + 6 i - 7 - 3 i$

Add $y i$ to both sides of the equation.

$2 x = - 4 + 6 i - 7 - 3 i + y i$

Subtract $7$ from $- 4$ .

$2 x = - 11 + 6 i - 3 i + y i$

Subtract $3 i$ from $6 i$ .

$2 x = - 11 + 3 i + y i$

Divide each term in $2 x = - 11 + 3 i + y i$ by $2$ and simplify.

Divide each term in $2 x = - 11 + 3 i + y i$ by $2$ .

$\frac{2 x}{2} = \frac{- 11}{2} + \frac{3 i}{2} + \frac{y i}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 11}{2} + \frac{3 i}{2} + \frac{y i}{2}$

Divide $x$ by $1$ .

$x = \frac{- 11}{2} + \frac{3 i}{2} + \frac{y i}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{11}{2} + \frac{3 i}{2} + \frac{y i}{2}$