Solve for y x(4-2y)=3y-1

$x (4 - 2 y) = 3 y - 1$

Step 1

Simplify $x (4 - 2 y)$ .

Rewrite.

$0 + 0 + x (4 - 2 y) = 3 y - 1$

Simplify by adding zeros.

$x (4 - 2 y) = 3 y - 1$

Apply the distributive property.

$x \cdot 4 + x (- 2 y) = 3 y - 1$

Reorder.

Move $4$ to the left of $x$ .

$4 \cdot x + x (- 2 y) = 3 y - 1$

Rewrite using the commutative property of multiplication.

$4 x - 2 x y = 3 y - 1$

Step 2

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

$4 x - 2 x y - 3 y = - 1$

Step 3

Subtract $4 x$ from both sides of the equation.

$- 2 x y - 3 y = - 1 - 4 x$

Step 4

Factor $y$ out of $- 2 x y - 3 y$ .

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

$y (- 2 x) - 3 y = - 1 - 4 x$

Factor $y$ out of $- 3 y$ .

$y (- 2 x) + y \cdot - 3 = - 1 - 4 x$

Factor $y$ out of $y (- 2 x) + y \cdot - 3$ .

$y (- 2 x - 3) = - 1 - 4 x$

Step 5

Divide each term in $y (- 2 x - 3) = - 1 - 4 x$ by $- 2 x - 3$ and simplify.

Divide each term in $y (- 2 x - 3) = - 1 - 4 x$ by $- 2 x - 3$ .

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

Simplify the left side.

Cancel the common factor of $- 2 x - 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Combine the numerators over the common denominator.

$y = \frac{- 1 - 4 x}{- 2 x - 3}$

Rewrite $- 1$ as $- 1 (1)$ .

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

Factor $- 1$ out of $- 4 x$ .

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

Factor $- 1$ out of $- 1 (1) - (4 x)$ .

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

Factor $- 1$ out of $- 2 x$ .

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

Rewrite $- 3$ as $- 1 (3)$ .

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

Factor $- 1$ out of $- (2 x) - 1 (3)$ .

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

Rewrite $- (2 x + 3)$ as $- 1 (2 x + 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{1 + 4 x}{2 x + 3}$

Solve for y x(4-2y)=3y-1

Related Questions

Support LCMGCF.com by disabling your adblocker.