Solve for x 9(x+1)=6-2(9x+7)

$9 (x + 1) = 6 - 2 (9 x + 7)$

Step 1

Simplify $9 (x + 1)$ .

Rewrite.

$0 + 0 + 9 (x + 1) = 6 - 2 (9 x + 7)$

Simplify by adding zeros.

$9 (x + 1) = 6 - 2 (9 x + 7)$

Apply the distributive property.

$9 x + 9 \cdot 1 = 6 - 2 (9 x + 7)$

Multiply $9$ by $1$ .

$9 x + 9 = 6 - 2 (9 x + 7)$

Step 2

Simplify $6 - 2 (9 x + 7)$ .

Simplify each term.

Apply the distributive property.

$9 x + 9 = 6 - 2 (9 x) - 2 \cdot 7$

Multiply $9$ by $- 2$ .

$9 x + 9 = 6 - 18 x - 2 \cdot 7$

Multiply $- 2$ by $7$ .

$9 x + 9 = 6 - 18 x - 14$

Subtract $14$ from $6$ .

$9 x + 9 = - 18 x - 8$

Step 3

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

Add $18 x$ to both sides of the equation.

$9 x + 9 + 18 x = - 8$

Add $9 x$ and $18 x$ .

$27 x + 9 = - 8$

Step 4

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

Subtract $9$ from both sides of the equation.

$27 x = - 8 - 9$

Subtract $9$ from $- 8$ .

$27 x = - 17$

Step 5

Divide each term in $27 x = - 17$ by $27$ and simplify.

Divide each term in $27 x = - 17$ by $27$ .

$\frac{27 x}{27} = \frac{- 17}{27}$

Simplify the left side.

Cancel the common factor of $27$ .

Cancel the common factor.

$\frac{27 x}{27} = \frac{- 17}{27}$

Divide $x$ by $1$ .

$x = \frac{- 17}{27}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{17}{27}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{17}{27}$

Decimal Form:

$x = - 0.\overline{629}$

Solve for x 9(x+1)=6-2(9x+7)

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