Evaluate 3x+1/2(2x+6)=6x+1

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

Step 1

Simplify $3 x + \frac{1}{2} \cdot (2 x + 6)$ .

Simplify each term.

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$3 x + x + 3 = 6 x + 1$

Add $3 x$ and $x$ .

$4 x + 3 = 6 x + 1$

Step 2

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

Subtract $6 x$ from both sides of the equation.

$4 x + 3 - 6 x = 1$

Subtract $6 x$ from $4 x$ .

$- 2 x + 3 = 1$

Step 3

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$- 2 x = 1 - 3$

Subtract $3$ from $1$ .

$- 2 x = - 2$

Step 4

Divide each term in $- 2 x = - 2$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 2$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 2}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 2}$

Simplify the right side.

Divide $- 2$ by $- 2$ .

$x = 1$

Evaluate 3x+1/2(2x+6)=6x+1

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