Solve for x 2x+3=1/2(4x+2)+2

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$2 x + 3 = 2 x + 1 + 2$

Add $1$ and $2$ .

$2 x + 3 = 2 x + 3$

Step 2

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 $3$ .

$3 = 3$

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:

$(- \infty, \infty)$