Simplify 4x+2-1/2x

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

Combine $x$ and $\frac{1}{2}$ .

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

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Simplify terms.

Combine $4 x$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $4 x \cdot 2 - x$ .

Factor $x$ out of $4 x \cdot 2$ .

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

Factor $x$ out of $- x$ .

$\frac{x (4 \cdot 2) + x \cdot - 1}{2} + 2$

Factor $x$ out of $x (4 \cdot 2) + x \cdot - 1$ .

$\frac{x (4 \cdot 2 - 1)}{2} + 2$

Multiply $4$ by $2$ .

$\frac{x (8 - 1)}{2} + 2$

Subtract $1$ from $8$ .

$\frac{x \cdot 7}{2} + 2$

Move $7$ to the left of $x$ .

$\frac{7 x}{2} + 2$