Solve for x 54-1/7yi=9x-4i

$54 - \frac{1}{7} y i = 9 x - 4 i$

Step 1

Rewrite the equation as $9 x - 4 i = 54 - \frac{1}{7} \cdot (y i)$ .

$9 x - 4 i = 54 - \frac{1}{7} \cdot (y i)$

Step 2

Multiply $- \frac{1}{7} (y i)$ .

Combine $y$ and $\frac{1}{7}$ .

$9 x - 4 i = 54 - \frac{y}{7} i$

Combine $i$ and $\frac{y}{7}$ .

$9 x - 4 i = 54 - \frac{i y}{7}$

Step 3

Add $4 i$ to both sides of the equation.

$9 x = 54 - \frac{i y}{7} + 4 i$

Step 4

Divide each term in $9 x = 54 - \frac{i y}{7} + 4 i$ by $9$ and simplify.

Divide each term in $9 x = 54 - \frac{i y}{7} + 4 i$ by $9$ .

$\frac{9 x}{9} = \frac{54}{9} + \frac{- \frac{i y}{7}}{9} + \frac{4 i}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{54}{9} + \frac{- \frac{i y}{7}}{9} + \frac{4 i}{9}$

Divide $x$ by $1$ .

$x = \frac{54}{9} + \frac{- \frac{i y}{7}}{9} + \frac{4 i}{9}$

Simplify the right side.

Simplify each term.

Divide $54$ by $9$ .

$x = 6 + \frac{- \frac{i y}{7}}{9} + \frac{4 i}{9}$

Multiply the numerator by the reciprocal of the denominator.

$x = 6 - \frac{i y}{7} \cdot \frac{1}{9} + \frac{4 i}{9}$

Multiply $- \frac{i y}{7} \cdot \frac{1}{9}$ .

Multiply $\frac{1}{9}$ by $\frac{i y}{7}$ .

$x = 6 - \frac{i y}{9 \cdot 7} + \frac{4 i}{9}$

Multiply $9$ by $7$ .

$x = 6 - \frac{i y}{63} + \frac{4 i}{9}$