Evaluate Using the Given Value 5x+y*7x-3y=-28

$5 x + y \cdot 7 x - 3 y = - 28$

Step 1

Rewrite using the commutative property of multiplication.

$5 x + 7 y x - 3 y = - 28$

Step 2

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

$5 x + 7 y x = - 28 + 3 y$

Step 3

Factor $x$ out of $5 x + 7 y x$ .

Factor $x$ out of $5 x$ .

$x \cdot 5 + 7 y x = - 28 + 3 y$

Factor $x$ out of $7 y x$ .

$x \cdot 5 + x (7 y) = - 28 + 3 y$

Factor $x$ out of $x \cdot 5 + x (7 y)$ .

$x (5 + 7 y) = - 28 + 3 y$

Step 4

Divide each term in $x (5 + 7 y) = - 28 + 3 y$ by $5 + 7 y$ and simplify.

Divide each term in $x (5 + 7 y) = - 28 + 3 y$ by $5 + 7 y$ .

$\frac{x (5 + 7 y)}{5 + 7 y} = \frac{- 28}{5 + 7 y} + \frac{3 y}{5 + 7 y}$

Simplify the left side.

Cancel the common factor of $5 + 7 y$ .

Cancel the common factor.

$\frac{x (5 + 7 y)}{5 + 7 y} = \frac{- 28}{5 + 7 y} + \frac{3 y}{5 + 7 y}$

Divide $x$ by $1$ .

$x = \frac{- 28}{5 + 7 y} + \frac{3 y}{5 + 7 y}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{- 28 + 3 y}{5 + 7 y}$

Rewrite $- 28$ as $- 1 (28)$ .

$x = \frac{- 1 (28) + 3 y}{5 + 7 y}$

Factor $- 1$ out of $3 y$ .

$x = \frac{- 1 (28) - (- 3 y)}{5 + 7 y}$

Factor $- 1$ out of $- 1 (28) - (- 3 y)$ .

$x = \frac{- 1 (28 - 3 y)}{5 + 7 y}$

Move the negative in front of the fraction.

$x = - \frac{28 - 3 y}{5 + 7 y}$