Solve x/a+1/2a=2x-3/2a+2(1-a)

$$\frac { x } { a } + \frac { 1 } { 2 } a = 2 x - \frac { 3 } { 2 } a + 2 ( 1 - a )$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=2a\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&a=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2a, the least common multiple of a,2.

$$2x+\frac{1}{2}a\times 2a=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Multiply a and a to get a^{2}.

$$2x+\frac{1}{2}a^{2}\times 2=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Multiply \frac{1}{2} and 2 to get 1.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Multiply a and a to get a^{2}.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

Multiply 2 and 2 to get 4.

$$2x+a^{2}=4xa-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

Multiply -\frac{3}{2} and 2 to get -3.

$$2x+a^{2}=4xa-3a^{2}+2\left(1-a\right)\times 2a$$

Multiply 2 and 2 to get 4.

$$2x+a^{2}=4xa-3a^{2}+4\left(1-a\right)a$$

Use the distributive property to multiply 4 by 1-a.

$$2x+a^{2}=4xa-3a^{2}+\left(4-4a\right)a$$

Use the distributive property to multiply 4-4a by a.

$$2x+a^{2}=4xa-3a^{2}+4a-4a^{2}$$

Combine -3a^{2} and -4a^{2} to get -7a^{2}.

$$2x+a^{2}=4xa-7a^{2}+4a$$

Subtract 4xa from both sides.

$$2x+a^{2}-4xa=-7a^{2}+4a$$

Subtract a^{2} from both sides.

$$2x-4xa=-7a^{2}+4a-a^{2}$$

Combine -7a^{2} and -a^{2} to get -8a^{2}.

$$2x-4xa=-8a^{2}+4a$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2-4a.

$$\frac{\left(2-4a\right)x}{2-4a}=\frac{4a\left(1-2a\right)}{2-4a}$$

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

$$x=\frac{4a\left(1-2a\right)}{2-4a}$$

Divide 4a\left(1-2a\right) by 2-4a.

$$x=2a$$

Solve for x

$$\left\{\begin{matrix}x=2a\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&a=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2a, the least common multiple of a,2.

$$2x+\frac{1}{2}a\times 2a=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Multiply a and a to get a^{2}.

$$2x+\frac{1}{2}a^{2}\times 2=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Multiply \frac{1}{2} and 2 to get 1.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a\times 2a+2\left(1-a\right)\times 2a$$

Multiply a and a to get a^{2}.

$$2x+a^{2}=2x\times 2a-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

Multiply 2 and 2 to get 4.

$$2x+a^{2}=4xa-\frac{3}{2}a^{2}\times 2+2\left(1-a\right)\times 2a$$

Multiply -\frac{3}{2} and 2 to get -3.

$$2x+a^{2}=4xa-3a^{2}+2\left(1-a\right)\times 2a$$

Multiply 2 and 2 to get 4.

$$2x+a^{2}=4xa-3a^{2}+4\left(1-a\right)a$$

Use the distributive property to multiply 4 by 1-a.

$$2x+a^{2}=4xa-3a^{2}+\left(4-4a\right)a$$

Use the distributive property to multiply 4-4a by a.

$$2x+a^{2}=4xa-3a^{2}+4a-4a^{2}$$

Combine -3a^{2} and -4a^{2} to get -7a^{2}.

$$2x+a^{2}=4xa-7a^{2}+4a$$

Subtract 4xa from both sides.

$$2x+a^{2}-4xa=-7a^{2}+4a$$

Subtract a^{2} from both sides.

$$2x-4xa=-7a^{2}+4a-a^{2}$$

Combine -7a^{2} and -a^{2} to get -8a^{2}.

$$2x-4xa=-8a^{2}+4a$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2-4a.

$$\frac{\left(2-4a\right)x}{2-4a}=\frac{4a\left(1-2a\right)}{2-4a}$$

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

$$x=\frac{4a\left(1-2a\right)}{2-4a}$$

Divide 4a\left(1-2a\right) by 2-4a.

$$x=2a$$

Solve for a

$$\left\{\begin{matrix}\\a=\frac{1}{2}=0.5\text{, }&\text{unconditionally}\\a=\frac{x}{2}\text{, }&x\neq 0\end{matrix}\right.$$