Solve 4xT+1=3t-7

$$4 x T + 1 = 3 t - 7$$

Solve for T (complex solution)

$$\left\{\begin{matrix}T=-\frac{8-3t}{4x}\text{, }&x\neq 0\\T\in \mathrm{C}\text{, }&t=\frac{8}{3}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 1 from both sides.

$$4xT=3t-7-1$$

Subtract 1 from -7 to get -8.

$$4xT=3t-8$$

Divide both sides by 4x.

$$\frac{4xT}{4x}=\frac{3t-8}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$T=\frac{3t-8}{4x}$$

Solve for T

$$\left\{\begin{matrix}T=-\frac{8-3t}{4x}\text{, }&x\neq 0\\T\in \mathrm{R}\text{, }&t=\frac{8}{3}\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 1 from both sides.

$$4xT=3t-7-1$$

Subtract 1 from -7 to get -8.

$$4xT=3t-8$$

Divide both sides by 4x.

$$\frac{4xT}{4x}=\frac{3t-8}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$T=\frac{3t-8}{4x}$$

Solve for t

$$t=\frac{4\left(Tx+2\right)}{3}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$3t-7=4xT+1$$

Add 7 to both sides.

$$3t=4xT+1+7$$

Add 1 and 7 to get 8.

$$3t=4xT+8$$

The equation is in standard form.

$$3t=4Tx+8$$

Divide both sides by 3.

$$\frac{3t}{3}=\frac{4Tx+8}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$t=\frac{4Tx+8}{3}$$