Solve for y 9x+18=6y-3x for y

$9 x + 18 = 6 y - 3 x$ for $y$

Step 1

Rewrite the equation as $6 y - 3 x = 9 x + 18$ .

$6 y - 3 x = 9 x + 18$

Step 2

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

Add $3 x$ to both sides of the equation.

$6 y = 9 x + 18 + 3 x$

Add $9 x$ and $3 x$ .

$6 y = 12 x + 18$

Step 3

Divide each term in $6 y = 12 x + 18$ by $6$ and simplify.

Divide each term in $6 y = 12 x + 18$ by $6$ .

$\frac{6 y}{6} = \frac{12 x}{6} + \frac{18}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{12 x}{6} + \frac{18}{6}$

Divide $y$ by $1$ .

$y = \frac{12 x}{6} + \frac{18}{6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $12$ and $6$ .

Factor $6$ out of $12 x$ .

$y = \frac{6 (2 x)}{6} + \frac{18}{6}$

Cancel the common factors.

Factor $6$ out of $6$ .

$y = \frac{6 (2 x)}{6 (1)} + \frac{18}{6}$

Cancel the common factor.

$y = \frac{6 (2 x)}{6 \cdot 1} + \frac{18}{6}$

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{18}{6}$

Divide $2 x$ by $1$ .

$y = 2 x + \frac{18}{6}$

Divide $18$ by $6$ .

$y = 2 x + 3$