Algebra Examples

$9 x - (5 x + 1) - (2 + 8 x - (7 x - 5)) + 9 x = 0$

Step 1

Simplify $9 x - (5 x + 1) - (2 + 8 x - (7 x - 5)) + 9 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$9 x - (5 x) - 1 \cdot 1 - (2 + 8 x - (7 x - 5)) + 9 x = 0$

Step 1.1.2

Multiply $5$ by $- 1$ .

$9 x - 5 x - 1 \cdot 1 - (2 + 8 x - (7 x - 5)) + 9 x = 0$

Step 1.1.3

Multiply $- 1$ by $1$ .

$9 x - 5 x - 1 - (2 + 8 x - (7 x - 5)) + 9 x = 0$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

Apply the distributive property.

$9 x - 5 x - 1 - (2 + 8 x - (7 x) - - 5) + 9 x = 0$

Step 1.1.4.2

Multiply $7$ by $- 1$ .

$9 x - 5 x - 1 - (2 + 8 x - 7 x - - 5) + 9 x = 0$

Step 1.1.4.3

Multiply $- 1$ by $- 5$ .

$9 x - 5 x - 1 - (2 + 8 x - 7 x + 5) + 9 x = 0$

Step 1.1.5

Add $2$ and $5$ .

$9 x - 5 x - 1 - (8 x - 7 x + 7) + 9 x = 0$

Step 1.1.6

Subtract $7 x$ from $8 x$ .

$9 x - 5 x - 1 - (x + 7) + 9 x = 0$

Step 1.1.7

Apply the distributive property.

$9 x - 5 x - 1 - x - 1 \cdot 7 + 9 x = 0$

Step 1.1.8

Multiply $- 1$ by $7$ .

$9 x - 5 x - 1 - x - 7 + 9 x = 0$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $5 x$ from $9 x$ .

$4 x - 1 - x - 7 + 9 x = 0$

Step 1.2.2

Subtract $x$ from $4 x$ .

$3 x - 1 - 7 + 9 x = 0$

Step 1.2.3

Add $3 x$ and $9 x$ .

$12 x - 1 - 7 = 0$

Step 1.2.4

Subtract $7$ from $- 1$ .

$12 x - 8 = 0$

Step 2

Add $8$ to both sides of the equation.

$12 x = 8$

Step 3

Divide each term in $12 x = 8$ by $12$ and simplify.

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Step 3.1

Divide each term in $12 x = 8$ by $12$ .

$\frac{12 x}{12} = \frac{8}{12}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $12$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{8}{12}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{12}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $8$ and $12$ .

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Step 3.3.1.1

Factor $4$ out of $8$ .

$x = \frac{4 (2)}{12}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $4$ out of $12$ .

$x = \frac{4 \cdot 2}{4 \cdot 3}$

Step 3.3.1.2.2

Cancel the common factor.

$x = \frac{4 \cdot 2}{4 \cdot 3}$

Step 3.3.1.2.3

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{6}$