Solve for x 9(3x+6)=14-(x+2)

$9 (3 x + 6) = 14 - (x + 2)$

Step 1

Simplify $9 (3 x + 6)$ .

Rewrite.

$0 + 0 + 9 (3 x + 6) = 14 - (x + 2)$

Simplify by adding zeros.

$9 (3 x + 6) = 14 - (x + 2)$

Apply the distributive property.

$9 (3 x) + 9 \cdot 6 = 14 - (x + 2)$

Multiply.

Multiply $3$ by $9$ .

$27 x + 9 \cdot 6 = 14 - (x + 2)$

Multiply $9$ by $6$ .

$27 x + 54 = 14 - (x + 2)$

Step 2

Simplify $14 - (x + 2)$ .

Simplify each term.

Apply the distributive property.

$27 x + 54 = 14 - x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$27 x + 54 = 14 - x - 2$

Subtract $2$ from $14$ .

$27 x + 54 = - x + 12$

Step 3

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

Add $x$ to both sides of the equation.

$27 x + 54 + x = 12$

Add $27 x$ and $x$ .

$28 x + 54 = 12$

Step 4

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

Subtract $54$ from both sides of the equation.

$28 x = 12 - 54$

Subtract $54$ from $12$ .

$28 x = - 42$

Step 5

Divide each term in $28 x = - 42$ by $28$ and simplify.

Divide each term in $28 x = - 42$ by $28$ .

$\frac{28 x}{28} = \frac{- 42}{28}$

Simplify the left side.

Cancel the common factor of $28$ .

Cancel the common factor.

$\frac{28 x}{28} = \frac{- 42}{28}$

Divide $x$ by $1$ .

$x = \frac{- 42}{28}$

Simplify the right side.

Cancel the common factor of $- 42$ and $28$ .

Factor $14$ out of $- 42$ .

$x = \frac{14 (- 3)}{28}$

Cancel the common factors.

Factor $14$ out of $28$ .

$x = \frac{14 \cdot - 3}{14 \cdot 2}$

Cancel the common factor.

$x = \frac{14 \cdot - 3}{14 \cdot 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 1.5$

Mixed Number Form:

$x = - 1 \frac{1}{2}$

Solve for x 9(3x+6)=14-(x+2)

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