Solve 4x+a*(x-1)=4

$$4 x + a \cdot ( x - 1 ) = 4$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=-4\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by x-1.

$$4x+ax-a=4$$

Subtract 4x from both sides.

$$ax-a=4-4x$$

Combine all terms containing a.

$$\left(x-1\right)a=4-4x$$

Divide both sides by -1+x.

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

Dividing by -1+x undoes the multiplication by -1+x.

$$a=\frac{4-4x}{x-1}$$

Divide 4-4x by -1+x.

$$a=-4$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&a=-4\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by x-1.

$$4x+ax-a=4$$

Add a to both sides.

$$4x+ax=4+a$$

Combine all terms containing x.

$$\left(4+a\right)x=4+a$$

The equation is in standard form.

$$\left(a+4\right)x=a+4$$

Divide both sides by 4+a.

$$\frac{\left(a+4\right)x}{a+4}=\frac{a+4}{a+4}$$

Dividing by 4+a undoes the multiplication by 4+a.

$$x=\frac{a+4}{a+4}$$

Divide 4+a by 4+a.

$$x=1$$

Solve for a

$$\left\{\begin{matrix}\\a=-4\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by x-1.

$$4x+ax-a=4$$

Subtract 4x from both sides.

$$ax-a=4-4x$$

Combine all terms containing a.

$$\left(x-1\right)a=4-4x$$

Divide both sides by -1+x.

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

Dividing by -1+x undoes the multiplication by -1+x.

$$a=\frac{4-4x}{x-1}$$

Divide 4-4x by -1+x.

$$a=-4$$

Solve for x

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&a=-4\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by x-1.

$$4x+ax-a=4$$

Add a to both sides.

$$4x+ax=4+a$$

Combine all terms containing x.

$$\left(4+a\right)x=4+a$$

The equation is in standard form.

$$\left(a+4\right)x=a+4$$

Divide both sides by 4+a.

$$\frac{\left(a+4\right)x}{a+4}=\frac{a+4}{a+4}$$

Dividing by 4+a undoes the multiplication by 4+a.

$$x=\frac{a+4}{a+4}$$

Divide 4+a by 4+a.

$$x=1$$