Finite Math Examples

$\frac{2 x}{9} + \frac{5}{9} = \frac{x - 1}{9}$

Step 1

Multiply both sides by $9$ .

$(\frac{2 x}{9} + \frac{5}{9}) \cdot 9 = \frac{x - 1}{9} \cdot 9$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{2 x}{9} + \frac{5}{9}) \cdot 9$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{2 x}{9} \cdot 9 + \frac{5}{9} \cdot 9 = \frac{x - 1}{9} \cdot 9$

Step 2.1.1.2

Cancel the common factor of $9$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{2 x}{9} \cdot 9 + \frac{5}{9} \cdot 9 = \frac{x - 1}{9} \cdot 9$

Step 2.1.1.2.2

Rewrite the expression.

$2 x + \frac{5}{9} \cdot 9 = \frac{x - 1}{9} \cdot 9$

Step 2.1.1.3

Cancel the common factor of $9$ .

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Step 2.1.1.3.1

Cancel the common factor.

$2 x + \frac{5}{9} \cdot 9 = \frac{x - 1}{9} \cdot 9$

Step 2.1.1.3.2

Rewrite the expression.

$2 x + 5 = \frac{x - 1}{9} \cdot 9$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

$2 x + 5 = \frac{x - 1}{9} \cdot 9$

Step 2.2.1.2

Rewrite the expression.

$2 x + 5 = x - 1$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$2 x + 5 - x = - 1$

Step 3.1.2

Subtract $x$ from $2 x$ .

$x + 5 = - 1$

Step 3.2

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

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Step 3.2.1

Subtract $5$ from both sides of the equation.

$x = - 1 - 5$

Step 3.2.2

Subtract $5$ from $- 1$ .

$x = - 6$