Solve x-a+x/3=1-2ax/5

$$x - \frac { a + x } { 3 } = \frac { 1 - 2 a x } { 5 }$$

Solve for a

$$a=-\frac{10x-3}{6x-5}$$

$$x\neq \frac{5}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$15x-5\left(a+x\right)=3\left(1-2ax\right)$$

Use the distributive property to multiply -5 by a+x.

$$15x-5a-5x=3\left(1-2ax\right)$$

Combine 15x and -5x to get 10x.

$$10x-5a=3\left(1-2ax\right)$$

Use the distributive property to multiply 3 by 1-2ax.

$$10x-5a=3-6xa$$

Add 6xa to both sides.

$$10x-5a+6xa=3$$

Subtract 10x from both sides.

$$-5a+6xa=3-10x$$

Combine all terms containing a.

$$\left(-5+6x\right)a=3-10x$$

The equation is in standard form.

$$\left(6x-5\right)a=3-10x$$

Divide both sides by -5+6x.

$$\frac{\left(6x-5\right)a}{6x-5}=\frac{3-10x}{6x-5}$$

Dividing by -5+6x undoes the multiplication by -5+6x.

$$a=\frac{3-10x}{6x-5}$$

Solve for x

$$x=\frac{5a+3}{2\left(3a+5\right)}$$

$$a\neq -\frac{5}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$15x-5\left(a+x\right)=3\left(1-2ax\right)$$

Use the distributive property to multiply -5 by a+x.

$$15x-5a-5x=3\left(1-2ax\right)$$

Combine 15x and -5x to get 10x.

$$10x-5a=3\left(1-2ax\right)$$

Use the distributive property to multiply 3 by 1-2ax.

$$10x-5a=3-6ax$$

Add 6ax to both sides.

$$10x-5a+6ax=3$$

Add 5a to both sides.

$$10x+6ax=3+5a$$

Combine all terms containing x.

$$\left(10+6a\right)x=3+5a$$

The equation is in standard form.

$$\left(6a+10\right)x=5a+3$$

Divide both sides by 10+6a.

$$\frac{\left(6a+10\right)x}{6a+10}=\frac{5a+3}{6a+10}$$

Dividing by 10+6a undoes the multiplication by 10+6a.

$$x=\frac{5a+3}{6a+10}$$

Divide 3+5a by 10+6a.

$$x=\frac{5a+3}{2\left(3a+5\right)}$$