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

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

Step 1

Simplify $2 x - \frac{3 x}{2}$ .

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $2 x \cdot 2 - 3 x$ .

Factor $x$ out of $2 x \cdot 2$ .

$\frac{x (2 \cdot 2) - 3 x}{2} = 4$

Factor $x$ out of $- 3 x$ .

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

Factor $x$ out of $x (2 \cdot 2) + x \cdot - 3$ .

$\frac{x (2 \cdot 2 - 3)}{2} = 4$

Multiply $2$ by $2$ .

$\frac{x (4 - 3)}{2} = 4$

Subtract $3$ from $4$ .

$\frac{x \cdot 1}{2} = 4$

Multiply $x$ by $1$ .

$\frac{x}{2} = 4$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 4$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 4$

Rewrite the expression.

$x = 2 \cdot 4$

Simplify the right side.

Multiply $2$ by $4$ .

$x = 8$