Solve for x (3x-4)/2+6=x-4

$\frac{3 x - 4}{2} + 6 = x - 4$

Step 1

Simplify $\frac{3 x - 4}{2} + 6$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x - 4}{2} + 6 \cdot \frac{2}{2} = x - 4$

Simplify terms.

Combine $6$ and $\frac{2}{2}$ .

$\frac{3 x - 4}{2} + \frac{6 \cdot 2}{2} = x - 4$

Combine the numerators over the common denominator.

$\frac{3 x - 4 + 6 \cdot 2}{2} = x - 4$

Simplify the numerator.

Multiply $6$ by $2$ .

$\frac{3 x - 4 + 12}{2} = x - 4$

Add $- 4$ and $12$ .

$\frac{3 x + 8}{2} = x - 4$

Step 2

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

Subtract $x$ from both sides of the equation.

$\frac{3 x + 8}{2} - x = - 4$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x + 8}{2} - x \cdot \frac{2}{2} = - 4$

Combine $- x$ and $\frac{2}{2}$ .

$\frac{3 x + 8}{2} + \frac{- x \cdot 2}{2} = - 4$

Combine the numerators over the common denominator.

$\frac{3 x + 8 - x \cdot 2}{2} = - 4$

Simplify the numerator.

Multiply $2$ by $- 1$ .

$\frac{3 x + 8 - 2 x}{2} = - 4$

Subtract $2 x$ from $3 x$ .

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

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{x + 8}{2} = 2 \cdot - 4$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x + 8}{2} = 2 \cdot - 4$

Rewrite the expression.

$x + 8 = 2 \cdot - 4$

Simplify the right side.

Multiply $2$ by $- 4$ .

$x + 8 = - 8$

Step 5

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

Subtract $8$ from both sides of the equation.

$x = - 8 - 8$

Subtract $8$ from $- 8$ .

$x = - 16$

Solve for x (3x-4)/2+6=x-4

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