Finite Math Examples

$\frac{x}{2} = \frac{99}{5} - 9 x$

Step 1

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 = (\frac{99}{5} - 9 x) \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{x}{2} \cdot 2 = (\frac{99}{5} - 9 x) \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$x = (\frac{99}{5} - 9 x) \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{99}{5} - 9 x) \cdot 2$ .

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Step 2.2.1.1

Apply the distributive property.

$x = \frac{99}{5} \cdot 2 - 9 x \cdot 2$

Step 2.2.1.2

Multiply $\frac{99}{5} \cdot 2$ .

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Step 2.2.1.2.1

Combine $\frac{99}{5}$ and $2$ .

$x = \frac{99 \cdot 2}{5} - 9 x \cdot 2$

Step 2.2.1.2.2

Multiply $99$ by $2$ .

$x = \frac{198}{5} - 9 x \cdot 2$

Step 2.2.1.3

Multiply $2$ by $- 9$ .

$x = \frac{198}{5} - 18 x$

Step 2.2.1.4

Reorder $\frac{198}{5}$ and $- 18 x$ .

$x = - 18 x + \frac{198}{5}$

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

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

$x + 18 x = \frac{198}{5}$

Step 3.1.2

Add $x$ and $18 x$ .

$19 x = \frac{198}{5}$

Step 3.2

Divide each term in $19 x = \frac{198}{5}$ by $19$ and simplify.

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Step 3.2.1

Divide each term in $19 x = \frac{198}{5}$ by $19$ .

$\frac{19 x}{19} = \frac{\frac{198}{5}}{19}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $19$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{19 x}{19} = \frac{\frac{198}{5}}{19}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{198}{5}}{19}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{198}{5} \cdot \frac{1}{19}$

Step 3.2.3.2

Multiply $\frac{198}{5} \cdot \frac{1}{19}$ .

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Step 3.2.3.2.1

Multiply $\frac{198}{5}$ by $\frac{1}{19}$ .

$x = \frac{198}{5 \cdot 19}$

Step 3.2.3.2.2

Multiply $5$ by $19$ .

$x = \frac{198}{95}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{198}{95}$

Decimal Form:

$x = 2.08421052 \dots$

Mixed Number Form:

$x = 2 \frac{8}{95}$