Solve 5xt+1=4t-5x

$$5 x t + 1 = 4 t - 5 x$$

Solve for t

$$t=-\frac{5x+1}{5x-4}$$

$$x\neq \frac{4}{5}$$

Steps for Solving Linear Equation

Subtract 4t from both sides.

$$5xt+1-4t=-5x$$

Subtract 1 from both sides.

$$5xt-4t=-5x-1$$

Combine all terms containing t.

$$\left(5x-4\right)t=-5x-1$$

Divide both sides by 5x-4.

$$\frac{\left(5x-4\right)t}{5x-4}=\frac{-5x-1}{5x-4}$$

Dividing by 5x-4 undoes the multiplication by 5x-4.

$$t=\frac{-5x-1}{5x-4}$$

Divide -5x-1 by 5x-4.

$$t=-\frac{5x+1}{5x-4}$$

Solve for x

$$x=-\frac{1-4t}{5\left(t+1\right)}$$

$$t\neq -1$$

Steps for Solving Linear Equation

Add 5x to both sides.

$$5xt+1+5x=4t$$

Subtract 1 from both sides.

$$5xt+5x=4t-1$$

Combine all terms containing x.

$$\left(5t+5\right)x=4t-1$$

Divide both sides by 5t+5.

$$\frac{\left(5t+5\right)x}{5t+5}=\frac{4t-1}{5t+5}$$

Dividing by 5t+5 undoes the multiplication by 5t+5.

$$x=\frac{4t-1}{5t+5}$$

Divide 4t-1 by 5t+5.

$$x=\frac{4t-1}{5\left(t+1\right)}$$