Finite Math Examples

$p = \frac{- 16}{20} x - 104.2$ , $p = \frac{- 16}{- 50} x - 11.88$

Step 1

Eliminate the equal sides of each equation and combine.

$- \frac{x \cdot 4}{5} - 104.2 = \frac{8}{25} x - 11.88$

Step 2

Solve $- \frac{x \cdot 4}{5} - 104.2 = \frac{8}{25} x - 11.88$ for $x$ .

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Step 2.1

Move $4$ to the left of $x$ .

$- \frac{4 x}{5} - 104.2 = \frac{8}{25} x - 11.88$

Step 2.2

Combine $\frac{8}{25}$ and $x$ .

$- \frac{4 x}{5} - 104.2 = \frac{8 x}{25} - 11.88$

Step 2.3

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

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Step 2.3.1

Subtract $\frac{8 x}{25}$ from both sides of the equation.

$- \frac{4 x}{5} - 104.2 - \frac{8 x}{25} = - 11.88$

Step 2.3.2

To write $- \frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{4 x}{5} \cdot \frac{5}{5} - \frac{8 x}{25} - 104.2 = - 11.88$

Step 2.3.3

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.3.1

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

$- \frac{4 x \cdot 5}{5 \cdot 5} - \frac{8 x}{25} - 104.2 = - 11.88$

Step 2.3.3.2

Multiply $5$ by $5$ .

$- \frac{4 x \cdot 5}{25} - \frac{8 x}{25} - 104.2 = - 11.88$

Step 2.3.4

Combine the numerators over the common denominator.

$\frac{- 4 x \cdot 5 - 8 x}{25} - 104.2 = - 11.88$

Step 2.3.5

Simplify each term.

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Step 2.3.5.1

Simplify the numerator.

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Step 2.3.5.1.1

Factor $4 x$ out of $- 4 x \cdot 5 - 8 x$ .

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Step 2.3.5.1.1.1

Factor $4 x$ out of $- 4 x \cdot 5$ .

$\frac{4 x (- 1 \cdot 5) - 8 x}{25} - 104.2 = - 11.88$

Step 2.3.5.1.1.2

Factor $4 x$ out of $- 8 x$ .

$\frac{4 x (- 1 \cdot 5) + 4 x (- 2)}{25} - 104.2 = - 11.88$

Step 2.3.5.1.1.3

Factor $4 x$ out of $4 x (- 1 \cdot 5) + 4 x (- 2)$ .

$\frac{4 x (- 1 \cdot 5 - 2)}{25} - 104.2 = - 11.88$

Step 2.3.5.1.2

Multiply $- 1$ by $5$ .

$\frac{4 x (- 5 - 2)}{25} - 104.2 = - 11.88$

Step 2.3.5.1.3

Subtract $2$ from $- 5$ .

$\frac{4 x \cdot - 7}{25} - 104.2 = - 11.88$

Step 2.3.5.1.4

Multiply $- 7$ by $4$ .

$\frac{- 28 x}{25} - 104.2 = - 11.88$

Step 2.3.5.2

Move the negative in front of the fraction.

$- \frac{28 x}{25} - 104.2 = - 11.88$

Step 2.4

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

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Step 2.4.1

Add $104.2$ to both sides of the equation.

$- \frac{28 x}{25} = - 11.88 + 104.2$

Step 2.4.2

Add $- 11.88$ and $104.2$ .

$- \frac{28 x}{25} = 92.32$

Step 2.5

Multiply both sides of the equation by $- \frac{25}{28}$ .

$- \frac{25}{28} (- \frac{28 x}{25}) = - \frac{25}{28} \cdot 92.32$

Step 2.6

Simplify both sides of the equation.

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Step 2.6.1

Simplify the left side.

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Step 2.6.1.1

Simplify $- \frac{25}{28} (- \frac{28 x}{25})$ .

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Step 2.6.1.1.1

Cancel the common factor of $25$ .

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Step 2.6.1.1.1.1

Move the leading negative in $- \frac{25}{28}$ into the numerator.

$\frac{- 25}{28} (- \frac{28 x}{25}) = - \frac{25}{28} \cdot 92.32$

Step 2.6.1.1.1.2

Move the leading negative in $- \frac{28 x}{25}$ into the numerator.

$\frac{- 25}{28} \cdot \frac{- 28 x}{25} = - \frac{25}{28} \cdot 92.32$

Step 2.6.1.1.1.3

Factor $25$ out of $- 25$ .

$\frac{25 (- 1)}{28} \cdot \frac{- 28 x}{25} = - \frac{25}{28} \cdot 92.32$

Step 2.6.1.1.1.4

Cancel the common factor.

$\frac{25 \cdot - 1}{28} \cdot \frac{- 28 x}{25} = - \frac{25}{28} \cdot 92.32$

Step 2.6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{28} (- 28 x) = - \frac{25}{28} \cdot 92.32$

Step 2.6.1.1.2

Cancel the common factor of $28$ .

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Step 2.6.1.1.2.1

Factor $28$ out of $- 28 x$ .

$\frac{- 1}{28} (28 (- x)) = - \frac{25}{28} \cdot 92.32$

Step 2.6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{28} (28 (- x)) = - \frac{25}{28} \cdot 92.32$

Step 2.6.1.1.2.3

Rewrite the expression.

$- - x = - \frac{25}{28} \cdot 92.32$

Step 2.6.1.1.3

Multiply.

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Step 2.6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{25}{28} \cdot 92.32$

Step 2.6.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{25}{28} \cdot 92.32$

Step 2.6.2

Simplify the right side.

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Step 2.6.2.1

Simplify $- \frac{25}{28} \cdot 92.32$ .

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Step 2.6.2.1.1

Multiply $- \frac{25}{28} \cdot 92.32$ .

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Step 2.6.2.1.1.1

Multiply $92.32$ by $- 1$ .

$x = - 92.32 (\frac{25}{28})$

Step 2.6.2.1.1.2

Combine $- 92.32$ and $\frac{25}{28}$ .

$x = \frac{- 92.32 \cdot 25}{28}$

Step 2.6.2.1.1.3

Multiply $- 92.32$ by $25$ .

$x = \frac{- 2308}{28}$

Step 2.6.2.1.2

Cancel the common factor of $- 2308$ and $28$ .

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Step 2.6.2.1.2.1

Factor $4$ out of $- 2308$ .

$x = \frac{4 (- 577)}{28}$

Step 2.6.2.1.2.2

Cancel the common factors.

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Step 2.6.2.1.2.2.1

Factor $4$ out of $28$ .

$x = \frac{4 \cdot - 577}{4 \cdot 7}$

Step 2.6.2.1.2.2.2

Cancel the common factor.

$x = \frac{4 \cdot - 577}{4 \cdot 7}$

Step 2.6.2.1.2.2.3

Rewrite the expression.

$x = \frac{- 577}{7}$

Step 2.6.2.1.3

Move the negative in front of the fraction.

$x = - \frac{577}{7}$

Step 3

Evaluate $p$ when $x = - \frac{577}{7}$ .

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Step 3.1

Substitute $- \frac{577}{7}$ for $x$ .

$p = \frac{8}{25} \cdot (- \frac{577}{7}) - 11.88$

Step 3.2

Substitute $- \frac{577}{7}$ for $x$ in $p = \frac{8}{25} \cdot (- \frac{577}{7}) - 11.88$ and solve for $p$ .

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Step 3.2.1

Remove parentheses.

$p = \frac{8}{25} \cdot (- 1 (\frac{577}{7})) - 11.88$

Step 3.2.2

Simplify $\frac{8}{25} \cdot (- 1 (\frac{577}{7})) - 11.88$ .

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Step 3.2.2.1

Simplify each term.

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Step 3.2.2.1.1

Rewrite $- 1 (\frac{577}{7})$ as $- (\frac{577}{7})$ .

$p = \frac{8}{25} \cdot (- (\frac{577}{7})) - 11.88$

Step 3.2.2.1.2

Multiply $\frac{8}{25} (- \frac{577}{7})$ .

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Step 3.2.2.1.2.1

Multiply $\frac{8}{25}$ by $\frac{577}{7}$ .

$p = - \frac{8 \cdot 577}{25 \cdot 7} - 11.88$

Step 3.2.2.1.2.2

Multiply $8$ by $577$ .

$p = - \frac{4616}{25 \cdot 7} - 11.88$

Step 3.2.2.1.2.3

Multiply $25$ by $7$ .

$p = - \frac{4616}{175} - 11.88$

Step 3.2.2.2

To write $- 11.88$ as a fraction with a common denominator, multiply by $\frac{175}{175}$ .

$p = - \frac{4616}{175} - 11.88 \cdot \frac{175}{175}$

Step 3.2.2.3

Combine $- 11.88$ and $\frac{175}{175}$ .

$p = - \frac{4616}{175} + \frac{- 11.88 \cdot 175}{175}$

Step 3.2.2.4

Combine the numerators over the common denominator.

$p = \frac{- 4616 - 11.88 \cdot 175}{175}$

Step 3.2.2.5

Simplify the numerator.

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Step 3.2.2.5.1

Multiply $- 11.88$ by $175$ .

$p = \frac{- 4616 - 2079}{175}$

Step 3.2.2.5.2

Subtract $2079$ from $- 4616$ .

$p = \frac{- 6695}{175}$

Step 3.2.2.6

Cancel the common factor of $- 6695$ and $175$ .

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Step 3.2.2.6.1

Factor $5$ out of $- 6695$ .

$p = \frac{5 (- 1339)}{175}$

Step 3.2.2.6.2

Cancel the common factors.

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Step 3.2.2.6.2.1

Factor $5$ out of $175$ .

$p = \frac{5 \cdot - 1339}{5 \cdot 35}$

Step 3.2.2.6.2.2

Cancel the common factor.

$p = \frac{5 \cdot - 1339}{5 \cdot 35}$

Step 3.2.2.6.2.3

Rewrite the expression.

$p = \frac{- 1339}{35}$

Step 3.2.2.7

Move the negative in front of the fraction.

$p = - \frac{1339}{35}$

Step 4

The solution of the system of equations is all the values that make the system true.

$p = - \frac{1339}{35}, x = - \frac{577}{7}$