Solve for x 2x+3=4x+6-(2x+3)

$2 x + 3 = 4 x + 6 - (2 x + 3)$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 x + 6 - (2 x + 3) = 2 x + 3$

Simplify $4 x + 6 - (2 x + 3)$ .

Simplify each term.

Apply the distributive property.

$4 x + 6 - (2 x) - 1 \cdot 3 = 2 x + 3$

Multiply $2$ by $- 1$ .

$4 x + 6 - 2 x - 1 \cdot 3 = 2 x + 3$

Multiply $- 1$ by $3$ .

$4 x + 6 - 2 x - 3 = 2 x + 3$

Simplify by adding terms.

Subtract $2 x$ from $4 x$ .

$2 x + 6 - 3 = 2 x + 3$

Subtract $3$ from $6$ .

$2 x + 3 = 2 x + 3$

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

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

$2 x + 3 - 2 x = 3$

Combine the opposite terms in $2 x + 3 - 2 x$ .

Subtract $2 x$ from $2 x$ .

$0 + 3 = 3$

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:

$(- \infty, \infty)$