Finite Math Examples

$7 x - 18 (\frac{6}{5}) = 6$

Step 1

Simplify each term.

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Step 1.1

Multiply $- 18 (\frac{6}{5})$ .

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Step 1.1.1

Combine $- 18$ and $\frac{6}{5}$ .

$7 x + \frac{- 18 \cdot 6}{5} = 6$

Step 1.1.2

Multiply $- 18$ by $6$ .

$7 x + \frac{- 108}{5} = 6$

Step 1.2

Move the negative in front of the fraction.

$7 x - \frac{108}{5} = 6$

Step 2

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

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Step 2.1

Add $\frac{108}{5}$ to both sides of the equation.

$7 x = 6 + \frac{108}{5}$

Step 2.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$7 x = 6 \cdot \frac{5}{5} + \frac{108}{5}$

Step 2.3

Combine $6$ and $\frac{5}{5}$ .

$7 x = \frac{6 \cdot 5}{5} + \frac{108}{5}$

Step 2.4

Combine the numerators over the common denominator.

$7 x = \frac{6 \cdot 5 + 108}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $6$ by $5$ .

$7 x = \frac{30 + 108}{5}$

Step 2.5.2

Add $30$ and $108$ .

$7 x = \frac{138}{5}$

Step 3

Divide each term in $7 x = \frac{138}{5}$ by $7$ and simplify.

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Step 3.1

Divide each term in $7 x = \frac{138}{5}$ by $7$ .

$\frac{7 x}{7} = \frac{\frac{138}{5}}{7}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{\frac{138}{5}}{7}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{138}{5}}{7}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{138}{5} \cdot \frac{1}{7}$

Step 3.3.2

Multiply $\frac{138}{5} \cdot \frac{1}{7}$ .

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Step 3.3.2.1

Multiply $\frac{138}{5}$ by $\frac{1}{7}$ .

$x = \frac{138}{5 \cdot 7}$

Step 3.3.2.2

Multiply $5$ by $7$ .

$x = \frac{138}{35}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{138}{35}$

Decimal Form:

$x = 3.94285714 \dots$

Mixed Number Form:

$x = 3 \frac{33}{35}$