Solve -6Ax+48x+7+B=24x+1

$$- 6 A x + 48 x + 7 + B = 24 x + 1$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{24x+B+6}{6x}\text{, }&x\neq 0\\A\in \mathrm{C}\text{, }&x=0\text{ and }B=-6\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 48x from both sides.

$$-6Ax+7+B=24x+1-48x$$

Combine 24x and -48x to get -24x.

$$-6Ax+7+B=-24x+1$$

Subtract 7 from both sides.

$$-6Ax+B=-24x+1-7$$

Subtract 7 from 1 to get -6.

$$-6Ax+B=-24x-6$$

Subtract B from both sides.

$$-6Ax=-24x-6-B$$

The equation is in standard form.

$$\left(-6x\right)A=-24x-B-6$$

Divide both sides by -6x.

$$\frac{\left(-6x\right)A}{-6x}=\frac{-24x-B-6}{-6x}$$

Dividing by -6x undoes the multiplication by -6x.

$$A=\frac{-24x-B-6}{-6x}$$

Divide -24x-B-6 by -6x.

$$A=\frac{\frac{B}{6}+1}{x}+4$$

Solve for A

$$\left\{\begin{matrix}A=\frac{24x+B+6}{6x}\text{, }&x\neq 0\\A\in \mathrm{R}\text{, }&x=0\text{ and }B=-6\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 48x from both sides.

$$-6Ax+7+B=24x+1-48x$$

Combine 24x and -48x to get -24x.

$$-6Ax+7+B=-24x+1$$

Subtract 7 from both sides.

$$-6Ax+B=-24x+1-7$$

Subtract 7 from 1 to get -6.

$$-6Ax+B=-24x-6$$

Subtract B from both sides.

$$-6Ax=-24x-6-B$$

The equation is in standard form.

$$\left(-6x\right)A=-24x-B-6$$

Divide both sides by -6x.

$$\frac{\left(-6x\right)A}{-6x}=\frac{-24x-B-6}{-6x}$$

Dividing by -6x undoes the multiplication by -6x.

$$A=\frac{-24x-B-6}{-6x}$$

Divide -24x-6-B by -6x.

$$A=\frac{\frac{B}{6}+1}{x}+4$$

Solve for B

$$B=6\left(Ax-4x-1\right)$$

Solution Steps

Add 6Ax to both sides.

$$48x+7+B=24x+1+6Ax$$

Subtract 48x from both sides.

$$7+B=24x+1+6Ax-48x$$

Combine 24x and -48x to get -24x.

$$7+B=-24x+1+6Ax$$

Subtract 7 from both sides.

$$B=-24x+1+6Ax-7$$

Subtract 7 from 1 to get -6.

$$B=-24x-6+6Ax$$