Finite Math Examples

$\frac{3}{5} \cdot (\frac{4}{5} x - \frac{1}{2}) = - \frac{3}{4}$

Step 1

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} (\frac{3}{5} \cdot (\frac{4}{5} x - \frac{1}{2})) = \frac{5}{3} (- \frac{3}{4})$

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 $\frac{5}{3} (\frac{3}{5} \cdot (\frac{4}{5} x - \frac{1}{2}))$ .

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Step 2.1.1.1

Combine $\frac{4}{5}$ and $x$ .

$\frac{5}{3} (\frac{3}{5} \cdot (\frac{4 x}{5} - \frac{1}{2})) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.2

Apply the distributive property.

$\frac{5}{3} (\frac{3}{5} \cdot \frac{4 x}{5} + \frac{3}{5} (- \frac{1}{2})) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.3

Multiply $\frac{3}{5} \cdot \frac{4 x}{5}$ .

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Step 2.1.1.3.1

Multiply $\frac{3}{5}$ by $\frac{4 x}{5}$ .

$\frac{5}{3} (\frac{3 (4 x)}{5 \cdot 5} + \frac{3}{5} (- \frac{1}{2})) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.3.2

Multiply $4$ by $3$ .

$\frac{5}{3} (\frac{12 x}{5 \cdot 5} + \frac{3}{5} (- \frac{1}{2})) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.3.3

Multiply $5$ by $5$ .

$\frac{5}{3} (\frac{12 x}{25} + \frac{3}{5} (- \frac{1}{2})) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.4

Multiply $\frac{3}{5} (- \frac{1}{2})$ .

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Step 2.1.1.4.1

Multiply $\frac{3}{5}$ by $\frac{1}{2}$ .

$\frac{5}{3} (\frac{12 x}{25} - \frac{3}{5 \cdot 2}) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.4.2

Multiply $5$ by $2$ .

$\frac{5}{3} (\frac{12 x}{25} - \frac{3}{10}) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.5

Apply the distributive property.

$\frac{5}{3} \cdot \frac{12 x}{25} + \frac{5}{3} (- \frac{3}{10}) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.6

Cancel the common factor of $5$ .

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Step 2.1.1.6.1

Factor $5$ out of $25$ .

$\frac{5}{3} \cdot \frac{12 x}{5 (5)} + \frac{5}{3} (- \frac{3}{10}) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{5}{3} \cdot \frac{12 x}{5 \cdot 5} + \frac{5}{3} (- \frac{3}{10}) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.6.3

Rewrite the expression.

$\frac{1}{3} \cdot \frac{12 x}{5} + \frac{5}{3} (- \frac{3}{10}) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.7

Cancel the common factor of $3$ .

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Step 2.1.1.7.1

Factor $3$ out of $12 x$ .

$\frac{1}{3} \cdot \frac{3 (4 x)}{5} + \frac{5}{3} (- \frac{3}{10}) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{1}{3} \cdot \frac{3 (4 x)}{5} + \frac{5}{3} (- \frac{3}{10}) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.7.3

Rewrite the expression.

$\frac{4 x}{5} + \frac{5}{3} (- \frac{3}{10}) = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.8

Cancel the common factor of $5$ .

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Step 2.1.1.8.1

Move the leading negative in $- \frac{3}{10}$ into the numerator.

$\frac{4 x}{5} + \frac{5}{3} \cdot \frac{- 3}{10} = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.8.2

Factor $5$ out of $10$ .

$\frac{4 x}{5} + \frac{5}{3} \cdot \frac{- 3}{5 (2)} = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.8.3

Cancel the common factor.

$\frac{4 x}{5} + \frac{5}{3} \cdot \frac{- 3}{5 \cdot 2} = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.8.4

Rewrite the expression.

$\frac{4 x}{5} + \frac{1}{3} \cdot \frac{- 3}{2} = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.9

Cancel the common factor of $3$ .

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Step 2.1.1.9.1

Factor $3$ out of $- 3$ .

$\frac{4 x}{5} + \frac{1}{3} \cdot \frac{3 (- 1)}{2} = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.9.2

Cancel the common factor.

$\frac{4 x}{5} + \frac{1}{3} \cdot \frac{3 \cdot - 1}{2} = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.9.3

Rewrite the expression.

$\frac{4 x}{5} + \frac{- 1}{2} = \frac{5}{3} (- \frac{3}{4})$

Step 2.1.1.10

Move the negative in front of the fraction.

$\frac{4 x}{5} - \frac{1}{2} = \frac{5}{3} (- \frac{3}{4})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{5}{3} (- \frac{3}{4})$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{4 x}{5} - \frac{1}{2} = \frac{5}{3} \cdot \frac{- 3}{4}$

Step 2.2.1.1.2

Factor $3$ out of $- 3$ .

$\frac{4 x}{5} - \frac{1}{2} = \frac{5}{3} \cdot \frac{3 (- 1)}{4}$

Step 2.2.1.1.3

Cancel the common factor.

$\frac{4 x}{5} - \frac{1}{2} = \frac{5}{3} \cdot \frac{3 \cdot - 1}{4}$

Step 2.2.1.1.4

Rewrite the expression.

$\frac{4 x}{5} - \frac{1}{2} = 5 (\frac{- 1}{4})$

Step 2.2.1.2

Combine $5$ and $\frac{- 1}{4}$ .

$\frac{4 x}{5} - \frac{1}{2} = \frac{5 \cdot - 1}{4}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $5$ by $- 1$ .

$\frac{4 x}{5} - \frac{1}{2} = \frac{- 5}{4}$

Step 2.2.1.3.2

Move the negative in front of the fraction.

$\frac{4 x}{5} - \frac{1}{2} = - \frac{5}{4}$

Step 3

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

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Step 3.1

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{4 x}{5} = - \frac{5}{4} + \frac{1}{2}$

Step 3.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x}{5} = - \frac{5}{4} + \frac{1}{2} \cdot \frac{2}{2}$

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{4 x}{5} = - \frac{5}{4} + \frac{2}{2 \cdot 2}$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{4 x}{5} = - \frac{5}{4} + \frac{2}{4}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{4 x}{5} = \frac{- 5 + 2}{4}$

Step 3.5

Add $- 5$ and $2$ .

$\frac{4 x}{5} = \frac{- 3}{4}$

Step 3.6

Move the negative in front of the fraction.

$\frac{4 x}{5} = - \frac{3}{4}$

Step 4

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} \cdot \frac{4 x}{5} = \frac{5}{4} (- \frac{3}{4})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{5}{4} \cdot \frac{4 x}{5}$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 x}{5} = \frac{5}{4} (- \frac{3}{4})$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 x) = \frac{5}{4} (- \frac{3}{4})$

Step 5.1.1.2

Cancel the common factor of $4$ .

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Step 5.1.1.2.1

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{5}{4} (- \frac{3}{4})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{5}{4} (- \frac{3}{4})$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{5}{4} (- \frac{3}{4})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{5}{4} (- \frac{3}{4})$ .

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Step 5.2.1.1

Multiply $\frac{5}{4}$ by $\frac{3}{4}$ .

$x = - \frac{5 \cdot 3}{4 \cdot 4}$

Step 5.2.1.2

Multiply $5$ by $3$ .

$x = - \frac{15}{4 \cdot 4}$

Step 5.2.1.3

Multiply $4$ by $4$ .

$x = - \frac{15}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{15}{16}$

Decimal Form:

$x = - 0.9375$