Solve for x 10x+5y+3=75

$10 x + 5 y + 3 = 75$

Step 1

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

Subtract $5 y$ from both sides of the equation.

$10 x + 3 = 75 - 5 y$

Subtract $3$ from both sides of the equation.

$10 x = 75 - 5 y - 3$

Subtract $3$ from $75$ .

$10 x = - 5 y + 72$

Step 2

Divide each term in $10 x = - 5 y + 72$ by $10$ and simplify.

Divide each term in $10 x = - 5 y + 72$ by $10$ .

$\frac{10 x}{10} = \frac{- 5 y}{10} + \frac{72}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{- 5 y}{10} + \frac{72}{10}$

Divide $x$ by $1$ .

$x = \frac{- 5 y}{10} + \frac{72}{10}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 5$ and $10$ .

Factor $5$ out of $- 5 y$ .

$x = \frac{5 (- y)}{10} + \frac{72}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$x = \frac{5 (- y)}{5 (2)} + \frac{72}{10}$

Cancel the common factor.

$x = \frac{5 (- y)}{5 \cdot 2} + \frac{72}{10}$

Rewrite the expression.

$x = \frac{- y}{2} + \frac{72}{10}$

Move the negative in front of the fraction.

$x = - \frac{y}{2} + \frac{72}{10}$

Cancel the common factor of $72$ and $10$ .

Factor $2$ out of $72$ .

$x = - \frac{y}{2} + \frac{2 (36)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$x = - \frac{y}{2} + \frac{2 \cdot 36}{2 \cdot 5}$

Cancel the common factor.

$x = - \frac{y}{2} + \frac{2 \cdot 36}{2 \cdot 5}$

Rewrite the expression.

$x = - \frac{y}{2} + \frac{36}{5}$