Algebra Examples

$\frac{6 x - 9}{3} = \frac{x}{9}$

Step 1

Cancel the common factor of $6 x - 9$ and $3$ .

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Step 1.1

Factor $3$ out of $6 x$ .

$\frac{3 (2 x) - 9}{3} = \frac{x}{9}$

Step 1.2

Factor $3$ out of $- 9$ .

$\frac{3 (2 x) + 3 \cdot - 3}{3} = \frac{x}{9}$

Step 1.3

Factor $3$ out of $3 (2 x) + 3 (- 3)$ .

$\frac{3 (2 x - 3)}{3} = \frac{x}{9}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $3$ .

$\frac{3 (2 x - 3)}{3 (1)} = \frac{x}{9}$

Step 1.4.2

Cancel the common factor.

$\frac{3 (2 x - 3)}{3 \cdot 1} = \frac{x}{9}$

Step 1.4.3

Rewrite the expression.

$\frac{2 x - 3}{1} = \frac{x}{9}$

Step 1.4.4

Divide $2 x - 3$ by $1$ .

$2 x - 3 = \frac{x}{9}$

$2 x - 3 = \frac{x}{9}$

$2 x - 3 = \frac{x}{9}$

Step 2

Solve for $x$ .

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Step 2.1

Multiply both sides by $9$ .

$(2 x - 3) \cdot 9 = \frac{x}{9} \cdot 9$

Step 2.2

Simplify.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Simplify $(2 x - 3) \cdot 9$ .

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Step 2.2.1.1.1

Apply the distributive property.

$2 x \cdot 9 - 3 \cdot 9 = \frac{x}{9} \cdot 9$

Step 2.2.1.1.2

Multiply.

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Step 2.2.1.1.2.1

Multiply $9$ by $2$ .

$18 x - 3 \cdot 9 = \frac{x}{9} \cdot 9$

Step 2.2.1.1.2.2

Multiply $- 3$ by $9$ .

$18 x - 27 = \frac{x}{9} \cdot 9$

$18 x - 27 = \frac{x}{9} \cdot 9$

$18 x - 27 = \frac{x}{9} \cdot 9$

$18 x - 27 = \frac{x}{9} \cdot 9$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Cancel the common factor of $9$ .

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Step 2.2.2.1.1

Cancel the common factor.

$18 x - 27 = \frac{x}{9} \cdot 9$

Step 2.2.2.1.2

Rewrite the expression.

$18 x - 27 = x$

$18 x - 27 = x$

$18 x - 27 = x$

$18 x - 27 = x$

Step 2.3

Solve for $x$ .

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Step 2.3.1

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

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Step 2.3.1.1

Subtract $x$ from both sides of the equation.

$18 x - 27 - x = 0$

Step 2.3.1.2

Subtract $x$ from $18 x$ .

$17 x - 27 = 0$

$17 x - 27 = 0$

Step 2.3.2

Add $27$ to both sides of the equation.

$17 x = 27$

Step 2.3.3

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

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Step 2.3.3.1

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

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

Step 2.3.3.2

Simplify the left side.

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Step 2.3.3.2.1

Cancel the common factor of $17$ .

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Step 2.3.3.2.1.1

Cancel the common factor.

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

Step 2.3.3.2.1.2

Divide $x$ by $1$ .

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

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

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

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

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.58823529 \dots$

Mixed Number Form:

$x = 1 \frac{10}{17}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$