Finite Math Examples

$\frac{1}{5} \cdot (5 x - 9) = 3$

Step 1

Multiply both sides of the equation by $5$ .

$5 (\frac{1}{5} \cdot (5 x - 9)) = 5 \cdot 3$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $5 (\frac{1}{5} \cdot (5 x - 9))$ .

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Step 2.1.1.1

Apply the distributive property.

$5 (\frac{1}{5} (5 x) + \frac{1}{5} \cdot - 9) = 5 \cdot 3$

Step 2.1.1.2

Cancel the common factor of $5$ .

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Step 2.1.1.2.1

Factor $5$ out of $5 x$ .

$5 (\frac{1}{5} (5 (x)) + \frac{1}{5} \cdot - 9) = 5 \cdot 3$

Step 2.1.1.2.2

Cancel the common factor.

$5 (\frac{1}{5} (5 x) + \frac{1}{5} \cdot - 9) = 5 \cdot 3$

Step 2.1.1.2.3

Rewrite the expression.

$5 (x + \frac{1}{5} \cdot - 9) = 5 \cdot 3$

Step 2.1.1.3

Combine $\frac{1}{5}$ and $- 9$ .

$5 (x + \frac{- 9}{5}) = 5 \cdot 3$

Step 2.1.1.4

Move the negative in front of the fraction.

$5 (x - \frac{9}{5}) = 5 \cdot 3$

Step 2.1.1.5

Apply the distributive property.

$5 x + 5 (- \frac{9}{5}) = 5 \cdot 3$

Step 2.1.1.6

Cancel the common factor of $5$ .

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Step 2.1.1.6.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$5 x + 5 (\frac{- 9}{5}) = 5 \cdot 3$

Step 2.1.1.6.2

Cancel the common factor.

$5 x + 5 (\frac{- 9}{5}) = 5 \cdot 3$

Step 2.1.1.6.3

Rewrite the expression.

$5 x - 9 = 5 \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $5$ by $3$ .

$5 x - 9 = 15$

Step 3

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

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Step 3.1

Add $9$ to both sides of the equation.

$5 x = 15 + 9$

Step 3.2

Add $15$ and $9$ .

$5 x = 24$

Step 4

Divide each term in $5 x = 24$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 x = 24$ by $5$ .

$\frac{5 x}{5} = \frac{24}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{24}{5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{24}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{24}{5}$

Decimal Form:

$x = 4.8$

Mixed Number Form:

$x = 4 \frac{4}{5}$