Solve for x (3x-8)/2=x-6

$\frac{3 x - 8}{2} = x - 6$

Step 1

Multiply both sides by $2$ .

$\frac{3 x - 8}{2} \cdot 2 = (x - 6) \cdot 2$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 x - 8}{2} \cdot 2 = (x - 6) \cdot 2$

Rewrite the expression.

$3 x - 8 = (x - 6) \cdot 2$

Simplify the right side.

Simplify $(x - 6) \cdot 2$ .

Apply the distributive property.

$3 x - 8 = x \cdot 2 - 6 \cdot 2$

Simplify the expression.

Move $2$ to the left of $x$ .

$3 x - 8 = 2 \cdot x - 6 \cdot 2$

Multiply $- 6$ by $2$ .

$3 x - 8 = 2 x - 12$

Step 3

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$3 x - 8 - 2 x = - 12$

Subtract $2 x$ from $3 x$ .

$x - 8 = - 12$

Move all terms not containing $x$ to the right side of the equation.

Add $8$ to both sides of the equation.

$x = - 12 + 8$

Add $- 12$ and $8$ .

$x = - 4$