Solve for x 2(x-3)=1/2(4x-12)

$2 (x - 3) = \frac{1}{2} (4 x - 12)$

Step 1

Simplify $2 (x - 3)$ .

Start simplifying.

$0 + 0 + 2 (x - 3) = \frac{1}{2} \cdot (4 x - 12)$

Simplify by adding zeros.

$2 (x - 3) = \frac{1}{2} \cdot (4 x - 12)$

Apply the distributive property.

$2 x + 2 \cdot - 3 = \frac{1}{2} \cdot (4 x - 12)$

Multiply $2$ by $- 3$ .

$2 x - 6 = \frac{1}{2} \cdot (4 x - 12)$

Step 2

Simplify $\frac{1}{2} \cdot (4 x - 12)$ .

Apply the distributive property.

$2 x - 6 = \frac{1}{2} (4 x) + \frac{1}{2} \cdot - 12$

Cancel the common factor of $2$ .

Factor $2$ out of $4 x$ .

$2 x - 6 = \frac{1}{2} (2 (2 x)) + \frac{1}{2} \cdot - 12$

Cancel the common factor.

$2 x - 6 = \frac{1}{2} (2 (2 x)) + \frac{1}{2} \cdot - 12$

Rewrite the expression.

$2 x - 6 = 2 x + \frac{1}{2} \cdot - 12$

Cancel the common factor of $2$ .

Factor $2$ out of $- 12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 x - 6 = 2 x - 6$

Step 3

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

Subtract $2 x$ from both sides of the equation.

$2 x - 6 - 2 x = - 6$

Combine the opposite terms in $2 x - 6 - 2 x$ .

Subtract $2 x$ from $2 x$ .

$0 - 6 = - 6$

Subtract $6$ from $0$ .

$- 6 = - 6$

Step 4

Since $- 6 = - 6$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Solve for x 2(x-3)=1/2(4x-12)

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