Solve x-a+2=2ax-3(a+x)-2(a-5)

$$x - a + 2 = 2 a x - 3 ( a + x ) - 2 ( a - 5 )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=2\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by a+x.

$$x-a+2=2ax-3a-3x-2\left(a-5\right)$$

Use the distributive property to multiply -2 by a-5.

$$x-a+2=2ax-3a-3x-2a+10$$

Combine -3a and -2a to get -5a.

$$x-a+2=2ax-5a-3x+10$$

Subtract 2ax from both sides.

$$x-a+2-2ax=-5a-3x+10$$

Add 5a to both sides.

$$x-a+2-2ax+5a=-3x+10$$

Combine -a and 5a to get 4a.

$$x+4a+2-2ax=-3x+10$$

Subtract x from both sides.

$$4a+2-2ax=-3x+10-x$$

Combine -3x and -x to get -4x.

$$4a+2-2ax=-4x+10$$

Subtract 2 from both sides.

$$4a-2ax=-4x+10-2$$

Subtract 2 from 10 to get 8.

$$4a-2ax=-4x+8$$

Combine all terms containing a.

$$\left(4-2x\right)a=-4x+8$$

The equation is in standard form.

$$\left(4-2x\right)a=8-4x$$

Divide both sides by 4-2x.

$$\frac{\left(4-2x\right)a}{4-2x}=\frac{8-4x}{4-2x}$$

Dividing by 4-2x undoes the multiplication by 4-2x.

$$a=\frac{8-4x}{4-2x}$$

Divide -4x+8 by 4-2x.

$$a=2$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&a=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by a+x.

$$x-a+2=2ax-3a-3x-2\left(a-5\right)$$

Use the distributive property to multiply -2 by a-5.

$$x-a+2=2ax-3a-3x-2a+10$$

Combine -3a and -2a to get -5a.

$$x-a+2=2ax-5a-3x+10$$

Subtract 2ax from both sides.

$$x-a+2-2ax=-5a-3x+10$$

Add 3x to both sides.

$$x-a+2-2ax+3x=-5a+10$$

Combine x and 3x to get 4x.

$$4x-a+2-2ax=-5a+10$$

Add a to both sides.

$$4x+2-2ax=-5a+10+a$$

Combine -5a and a to get -4a.

$$4x+2-2ax=-4a+10$$

Subtract 2 from both sides.

$$4x-2ax=-4a+10-2$$

Subtract 2 from 10 to get 8.

$$4x-2ax=-4a+8$$

Combine all terms containing x.

$$\left(4-2a\right)x=-4a+8$$

The equation is in standard form.

$$\left(4-2a\right)x=8-4a$$

Divide both sides by 4-2a.

$$\frac{\left(4-2a\right)x}{4-2a}=\frac{8-4a}{4-2a}$$

Dividing by 4-2a undoes the multiplication by 4-2a.

$$x=\frac{8-4a}{4-2a}$$

Divide -4a+8 by 4-2a.

$$x=2$$

Solve for a

$$\left\{\begin{matrix}\\a=2\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by a+x.

$$x-a+2=2ax-3a-3x-2\left(a-5\right)$$

Use the distributive property to multiply -2 by a-5.

$$x-a+2=2ax-3a-3x-2a+10$$

Combine -3a and -2a to get -5a.

$$x-a+2=2ax-5a-3x+10$$

Subtract 2ax from both sides.

$$x-a+2-2ax=-5a-3x+10$$

Add 5a to both sides.

$$x-a+2-2ax+5a=-3x+10$$

Combine -a and 5a to get 4a.

$$x+4a+2-2ax=-3x+10$$

Subtract x from both sides.

$$4a+2-2ax=-3x+10-x$$

Combine -3x and -x to get -4x.

$$4a+2-2ax=-4x+10$$

Subtract 2 from both sides.

$$4a-2ax=-4x+10-2$$

Subtract 2 from 10 to get 8.

$$4a-2ax=-4x+8$$

Combine all terms containing a.

$$\left(4-2x\right)a=-4x+8$$

The equation is in standard form.

$$\left(4-2x\right)a=8-4x$$

Divide both sides by 4-2x.

$$\frac{\left(4-2x\right)a}{4-2x}=\frac{8-4x}{4-2x}$$

Dividing by 4-2x undoes the multiplication by 4-2x.

$$a=\frac{8-4x}{4-2x}$$

Divide -4x+8 by 4-2x.

$$a=2$$

Solve for x

$$\left\{\begin{matrix}\\x=2\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&a=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by a+x.

$$x-a+2=2ax-3a-3x-2\left(a-5\right)$$

Use the distributive property to multiply -2 by a-5.

$$x-a+2=2ax-3a-3x-2a+10$$

Combine -3a and -2a to get -5a.

$$x-a+2=2ax-5a-3x+10$$

Subtract 2ax from both sides.

$$x-a+2-2ax=-5a-3x+10$$

Add 3x to both sides.

$$x-a+2-2ax+3x=-5a+10$$

Combine x and 3x to get 4x.

$$4x-a+2-2ax=-5a+10$$

Add a to both sides.

$$4x+2-2ax=-5a+10+a$$

Combine -5a and a to get -4a.

$$4x+2-2ax=-4a+10$$

Subtract 2 from both sides.

$$4x-2ax=-4a+10-2$$

Subtract 2 from 10 to get 8.

$$4x-2ax=-4a+8$$

Combine all terms containing x.

$$\left(4-2a\right)x=-4a+8$$

The equation is in standard form.

$$\left(4-2a\right)x=8-4a$$

Divide both sides by 4-2a.

$$\frac{\left(4-2a\right)x}{4-2a}=\frac{8-4a}{4-2a}$$

Dividing by 4-2a undoes the multiplication by 4-2a.

$$x=\frac{8-4a}{4-2a}$$

Divide -4a+8 by 4-2a.

$$x=2$$