Solve for x 1/2(2x-6)=x-3

$\frac{1}{2} (2 x - 6) = x - 3$

Step 1

Simplify $\frac{1}{2} \cdot (2 x - 6)$ .

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (2 x - 6) = x - 3$

Simplify by adding zeros.

$\frac{1}{2} \cdot (2 x - 6) = x - 3$

Apply the distributive property.

$\frac{1}{2} (2 x) + \frac{1}{2} \cdot - 6 = x - 3$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) + \frac{1}{2} \cdot - 6 = x - 3$

Cancel the common factor.

$\frac{1}{2} (2 x) + \frac{1}{2} \cdot - 6 = x - 3$

Rewrite the expression.

$x + \frac{1}{2} \cdot - 6 = x - 3$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x - 3 = x - 3$

Step 2

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

Subtract $x$ from both sides of the equation.

$x - 3 - x = - 3$

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

Subtract $x$ from $x$ .

$0 - 3 = - 3$

Subtract $3$ from $0$ .

$- 3 = - 3$

Step 3

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

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$