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

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

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

Cancel the common factor of $2 x + 6$ and $2$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $6$ .

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

Factor $2$ out of $2 (x) + 2 (3)$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $x + 3$ by $1$ .

$x + 3 - x = 3$

Combine the opposite terms in $x + 3 - x$ .

Subtract $x$ from $x$ .

$0 + 3 = 3$

Add $0$ and $3$ .

$3 = 3$

Since $3 = 3$ , the equation will always be true for any value of $x$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$