Solve 2x+a(x+3)=2a

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

Solve for a

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

$$x\neq -1$$

Steps for Solving Linear Equation

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

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

Subtract 2a from both sides.

$$2x+ax+3a-2a=0$$

Combine 3a and -2a to get a.

$$2x+ax+a=0$$

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$ax+a=-2x$$

Combine all terms containing a.

$$\left(x+1\right)a=-2x$$

Divide both sides by x+1.

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

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

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

Solve for x

$$x=-\frac{a}{a+2}$$

$$a\neq -2$$

Steps for Solving Linear Equation

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

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

Subtract 3a from both sides.

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

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

$$2x+ax=-a$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 2+a.

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

Dividing by 2+a undoes the multiplication by 2+a.

$$x=-\frac{a}{a+2}$$