Solve for x 3(x+4)-2(2+2x)=3(x-6x+12+2)

$3 (x + 4) - 2 (2 + 2 x) = 3 (x - 6 x + 12 + 2)$

Step 1

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

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot 4 - 2 (2 + 2 x) = 3 (x - 6 x + 12 + 2)$

Multiply $3$ by $4$ .

$3 x + 12 - 2 (2 + 2 x) = 3 (x - 6 x + 12 + 2)$

Apply the distributive property.

$3 x + 12 - 2 \cdot 2 - 2 (2 x) = 3 (x - 6 x + 12 + 2)$

Multiply $- 2$ by $2$ .

$3 x + 12 - 4 - 2 (2 x) = 3 (x - 6 x + 12 + 2)$

Multiply $2$ by $- 2$ .

$3 x + 12 - 4 - 4 x = 3 (x - 6 x + 12 + 2)$

Simplify by adding terms.

Subtract $4 x$ from $3 x$ .

$- x + 12 - 4 = 3 (x - 6 x + 12 + 2)$

Subtract $4$ from $12$ .

$- x + 8 = 3 (x - 6 x + 12 + 2)$

Step 2

Simplify $3 (x - 6 x + 12 + 2)$ .

Subtract $6 x$ from $x$ .

$- x + 8 = 3 (- 5 x + 12 + 2)$

Add $12$ and $2$ .

$- x + 8 = 3 (- 5 x + 14)$

Apply the distributive property.

$- x + 8 = 3 (- 5 x) + 3 \cdot 14$

Multiply.

Multiply $- 5$ by $3$ .

$- x + 8 = - 15 x + 3 \cdot 14$

Multiply $3$ by $14$ .

$- x + 8 = - 15 x + 42$

Step 3

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

Add $15 x$ to both sides of the equation.

$- x + 8 + 15 x = 42$

Add $- x$ and $15 x$ .

$14 x + 8 = 42$

Step 4

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

Subtract $8$ from both sides of the equation.

$14 x = 42 - 8$

Subtract $8$ from $42$ .

$14 x = 34$

Step 5

Divide each term in $14 x = 34$ by $14$ and simplify.

Divide each term in $14 x = 34$ by $14$ .

$\frac{14 x}{14} = \frac{34}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} = \frac{34}{14}$

Divide $x$ by $1$ .

$x = \frac{34}{14}$

Simplify the right side.

Cancel the common factor of $34$ and $14$ .

Factor $2$ out of $34$ .

$x = \frac{2 (17)}{14}$

Cancel the common factors.

Factor $2$ out of $14$ .

$x = \frac{2 \cdot 17}{2 \cdot 7}$

Cancel the common factor.

$x = \frac{2 \cdot 17}{2 \cdot 7}$

Rewrite the expression.

$x = \frac{17}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{17}{7}$

Decimal Form:

$x = 2.\overline{428571}$

Mixed Number Form:

$x = 2 \frac{3}{7}$

Solve for x 3(x+4)-2(2+2x)=3(x-6x+12+2)

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