Solve for t 7t+3x=4t-5y

$7 t + 3 x = 4 t - 5 y$

Step 1

Move all terms containing $t$ to the left side of the equation.

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

$7 t + 3 x - 4 t = - 5 y$

Subtract $4 t$ from $7 t$ .

$3 t + 3 x = - 5 y$

Step 2

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

$3 t = - 5 y - 3 x$

Step 3

Divide each term in $3 t = - 5 y - 3 x$ by $3$ and simplify.

Divide each term in $3 t = - 5 y - 3 x$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $t$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Cancel the common factor of $- 3$ and $3$ .

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

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

$t = - \frac{5 y}{3} + \frac{3 (- x)}{3 \cdot 1}$

Rewrite the expression.

$t = - \frac{5 y}{3} + \frac{- x}{1}$

Divide $- x$ by $1$ .

$t = - \frac{5 y}{3} - x$