Solve for x 4x+5y=10

$4 x + 5 y = 10$

Step 1

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

$4 x = 10 - 5 y$

Step 2

Divide each term in $4 x = 10 - 5 y$ by $4$ and simplify.

Divide each term in $4 x = 10 - 5 y$ by $4$ .

$\frac{4 x}{4} = \frac{10}{4} + \frac{- 5 y}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{10}{4} + \frac{- 5 y}{4}$

Divide $x$ by $1$ .

$x = \frac{10}{4} + \frac{- 5 y}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{4} + \frac{- 5 y}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 5}{2 \cdot 2} + \frac{- 5 y}{4}$

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot 2} + \frac{- 5 y}{4}$

Rewrite the expression.

$x = \frac{5}{2} + \frac{- 5 y}{4}$

Move the negative in front of the fraction.

$x = \frac{5}{2} - \frac{5 y}{4}$