Solve for x (4-x)/2+3x=1/2

$\frac{4 - x}{2} + 3 x = \frac{1}{2}$

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

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 - x}{2} + 3 x \cdot \frac{2}{2} = \frac{1}{2}$

Simplify terms.

Combine $3 x$ and $\frac{2}{2}$ .

$\frac{4 - x}{2} + \frac{3 x \cdot 2}{2} = \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{4 - x + 3 x \cdot 2}{2} = \frac{1}{2}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{4 - x + 6 x}{2} = \frac{1}{2}$

Add $- x$ and $6 x$ .

$\frac{4 + 5 x}{2} = \frac{1}{2}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$4 + 5 x = 1$

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

Subtract $4$ from both sides of the equation.

$5 x = 1 - 4$

Subtract $4$ from $1$ .

$5 x = - 3$

Divide each term in $5 x = - 3$ by $5$ and simplify.

Divide each term in $5 x = - 3$ by $5$ .

$\frac{5 x}{5} = \frac{- 3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 3}{5}$

Divide $x$ by $1$ .

$x = \frac{- 3}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{5}$

Decimal Form:

$x = - 0.6$